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placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="17">Φ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="2"> <ml:real>1</ml:real> <ml:real>-0.070123541776235282</ml:real> <ml:real>0.21773359721521066</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="43"/> </region> <region region-id="688" left="6" top="2430.75" width="200.25" height="29.25" align-x="24.75" align-y="2448" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">augment</ml:id> <ml:sequence> <ml:id xml:space="preserve" font="17" subscript="1">X</ml:id> <ml:id xml:space="preserve" font="17" subscript="2">X</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="2"> <ml:real>0.90598075894246666</ml:real> <ml:real>-0.063530579598167408</ml:real> <ml:real>0.11194729902666507</ml:real> <ml:real>0.51414802519436142</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="87" left="6" top="2476.5" width="90.75" height="31.5" align-x="54.75" align-y="2496" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve" font="17">Φ</ml:id> </ml:apply> <ml:id xml:space="preserve" font="17">J</ml:id> </ml:apply> <ml:id xml:space="preserve" font="17">Φ</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="2"> <ml:real>1</ml:real> <ml:real>4.163336342344337E-17</ml:real> <ml:real>5.5511151231257827E-17</ml:real> <ml:real>0.99999999999999978</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="45"/> </region> <region region-id="689" left="12" top="2530.5" width="170.25" height="31.5" align-x="33.75" align-y="2550" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="17">W</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve" font="17">Φ</ml:id> </ml:apply> <ml:id xml:space="preserve" font="17">K</ml:id> </ml:apply> <ml:id xml:space="preserve" font="17">Φ</ml:id> </ml:apply> <result 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>163.5366277806996</ml:real> </result> </ml:eval> </math> <rendering item-idref="47"/> </region> <region region-id="626" left="372" top="2535" width="66.75" height="24" align-x="400.5" align-y="2550" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>39.1928408183342</ml:real> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="99" left="6" top="2681.25" width="120" height="15.75" align-x="34.5" align-y="2694" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Forzante (costante) </p> </text> </region> <region region-id="101" left="6" top="2721" width="36" height="12.75" align-x="20.25" align-y="2730" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">F</ml:id> <ml:real>500</ml:real> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="627" left="6" top="2748.75" width="53.25" height="29.25" align-x="23.25" align-y="2766" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="17">F</ml:id> <ml:matrix rows="2" cols="1"> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">F</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="628" left="156" top="2748.75" width="55.5" height="29.25" align-x="171.75" align-y="2766" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="17">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:real>0</ml:real> <ml:real>110</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="51"/> </region> <region region-id="110" left="6" top="2818.5" width="101.25" height="31.5" align-x="28.5" align-y="2838" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve" font="17">Φ</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="2"> <ml:real>0.90598075894246666</ml:real> <ml:real>0.11194729902666507</ml:real> <ml:real>-0.063530579598167408</ml:real> <ml:real>0.51414802519436142</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="52"/> </region> <region region-id="111" left="6" top="2866.5" width="114" height="31.5" align-x="24.75" align-y="2886" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve" font="17">Φ</ml:id> </ml:apply> <ml:id xml:space="preserve" font="17">F</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:real>-6.9883637557984146</ml:real> <ml:real>56.556282771379756</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="115" left="6" top="2939.25" width="453.75" height="19.5" align-x="39" align-y="2952" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Equazioni di moto in formato matriciale (nelle coord. principali p<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>1</sub> </c> </inlineAttr> </f> e p<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>2</sub> </c> </inlineAttr> </f>)</p> </text> </region> <region region-id="631" left="6" top="2971.5" width="192" height="51.75" align-x="165.75" align-y="3000" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:id xml:space="preserve" subscript="1">p''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">p''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> <ml:apply> <ml:mult/> <ml:matrix rows="2" cols="2"> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:matrix> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:id xml:space="preserve" subscript="1">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> </ml:apply> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve" subscript="1">Q</ml:id> <ml:id xml:space="preserve" subscript="2">Q</ml:id> </ml:matrix> </ml:apply> </math> <rendering item-idref="54"/> </region> <region region-id="150" left="6" top="3071.25" width="558.75" height="19.5" align-x="39" align-y="3084" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Equazioni differenziali scritte separatamente nelle coordinate principali p<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>1</sub> </c> </inlineAttr> </f>(t) e p<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>2</sub> </c> </inlineAttr> </f>(t)</p> </text> </region> <region region-id="641" left="6" top="3111" width="107.25" height="22.5" align-x="93.75" align-y="3126" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="1">p''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">Q</ml:id> </ml:apply> </math> <rendering item-idref="55"/> </region> <region region-id="640" left="366" top="3111" width="71.25" height="24" align-x="394.5" align-y="3126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>163.5366277806996</ml:real> </result> </ml:eval> </math> <rendering item-idref="56"/> </region> <region region-id="639" left="570" top="3111.75" width="60.75" height="20.25" align-x="591.75" align-y="3126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-6.9883637557984146</ml:real> </result> </ml:eval> </math> <rendering item-idref="57"/> </region> <region region-id="636" left="6" top="3153" width="107.25" height="22.5" align-x="93.75" align-y="3168" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="2">p''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">Q</ml:id> </ml:apply> </math> <rendering item-idref="58"/> </region> <region region-id="638" left="366" top="3153" width="66.75" height="24" align-x="394.5" align-y="3168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>39.1928408183342</ml:real> </result> </ml:eval> </math> <rendering item-idref="59"/> </region> <region region-id="637" left="570" top="3153.75" width="60" height="20.25" align-x="591.75" align-y="3168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>56.556282771379756</ml:real> </result> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="647" left="6" top="3189" width="68.25" height="36.75" align-x="30.75" align-y="3210" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:id xml:space="preserve" subscript="1">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> </ml:apply> </math> <rendering item-idref="61"/> </region> <region region-id="323" left="6" top="3335.25" width="537" height="15.75" align-x="36.75" align-y="3348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Soluzione delle equazioni in coord. principali (dalla teoria dei sistemi a 1 gdl non smorzati):</p> </text> </region> <region region-id="177" left="6" top="3372.75" width="192.75" height="46.5" align-x="34.5" align-y="3396" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="1">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="62"/> </region> <region region-id="648" left="6" top="3438.75" width="192.75" height="46.5" align-x="34.5" align-y="3462" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="2">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="63"/> </region> <region region-id="406" left="6" top="3557.25" width="468.75" height="15.75" align-x="33" align-y="3570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Derivate temporali prime (velocità); sono state calcolate a mano, per semplicità</p> </text> </region> <region region-id="649" left="6" top="3585" width="190.5" height="18" align-x="36.75" align-y="3594" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="1">p'</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">A</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="1">B</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="64"/> </region> <region region-id="650" left="6" top="3621" width="190.5" height="18" align-x="36.75" align-y="3630" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="2">p'</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">A</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">B</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="65"/> </region> <region region-id="651" left="6" top="3659.25" width="460.5" height="19.5" align-x="31.5" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Occorre assegnare le condizioni iniziali per calcolare le costanti A<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>1</sub> </c> </inlineAttr> </f>, B<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>1</sub> </c> </inlineAttr> </f>, A<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>2</sub> </c> </inlineAttr> </f>, B<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub> <f family="Arial" charset="0" size="14">2</f> </sub> </c> </inlineAttr> </p> </text> </region> <region region-id="652" left="6" top="3713.25" width="746.25" height="47.25" align-x="13.5" align-y="3726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial Baltic" charset="186">Le condizioni iniziali </f> <f family="Arial Baltic" charset="186"> <u>vengono sempre assegnate nelle coordinate fisiche</u> </f> <f family="Arial Baltic" charset="186">; occorre quindi convertirle nelle coordinate principali.</f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial Baltic" charset="186">Si utilizzano le seguenti trasformazioni:</f> </p> </text> </region> <region region-id="653" left="6" top="3813.75" width="78" height="25.5" align-x="30.75" align-y="3834" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" font="17">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="66"/> </region> <region region-id="654" left="210" top="3821.25" width="89.25" height="15.75" align-x="221.25" align-y="3834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">per le posizioni</p> </text> </region> <region region-id="657" left="6" top="3849.75" width="87" height="25.5" align-x="35.25" align-y="3870" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">p'</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" font="17">x'</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="67"/> </region> <region region-id="658" left="210" top="3857.25" width="83.25" height="15.75" align-x="221.25" align-y="3870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">per le velocità</p> </text> </region> <region region-id="275" left="6" top="3917.25" width="171" height="15.75" align-x="6" align-y="3930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">All'istante iniziale t=0 si avrà:</p> </text> </region> <region region-id="667" left="6" top="3957.75" width="79.5" height="25.5" align-x="31.5" align-y="3978" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">p</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" font="17">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="68"/> </region> <region region-id="668" left="6" top="3993.75" width="88.5" height="25.5" align-x="36" align-y="4014" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">p'</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" font="17">x'</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="69"/> </region> <region region-id="293" left="6" top="4067.25" width="330.75" height="15.75" align-x="6" align-y="4080" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Assegniamo le condizioni iniziali nelle coordinate fisiche</p> </text> </region> <region region-id="670" left="6" top="4101" width="57" height="36.75" align-x="30.75" align-y="4122" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve" subscript="0">α</ml:id> <ml:id xml:space="preserve" subscript="0">β</ml:id> </ml:matrix> </ml:apply> </math> <rendering item-idref="70"/> </region> <region region-id="672" left="6" top="4149" width="63.75" height="36.75" align-x="35.25" align-y="4170" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">x'</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve" subscript="0">α'</ml:id> <ml:id xml:space="preserve" subscript="0">β'</ml:id> </ml:matrix> </ml:apply> </math> <rendering item-idref="71"/> </region> <region region-id="407" left="6" top="4227" width="105" height="16.5" align-x="24" align-y="4236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">α</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">rad</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.3490658503988659</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="radian"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="72"/> </region> <region region-id="408" left="270" top="4227" width="105.75" height="16.5" align-x="288.75" align-y="4236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">β</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">rad</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.17453292519943295</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="radian"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="409" left="6" top="4281" width="33" height="16.5" align-x="26.25" align-y="4290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">α'</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="74"/> </region> <region region-id="410" left="270" top="4281" width="39" height="16.5" align-x="291" align-y="4290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">β'</ml:id> <ml:real>-3</ml:real> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="322" left="6" top="4361.25" width="348.75" height="15.75" align-x="6" align-y="4374" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Convertiamo le condizioni iniziali nelle coordinate principali</p> </text> </region> <region region-id="325" left="6" top="4403.25" width="94.5" height="15.75" align-x="17.25" align-y="4416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Per le posizioni:</p> </text> </region> <region region-id="308" left="6" top="4443.75" width="79.5" height="25.5" align-x="31.5" align-y="4464" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">p</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" font="17">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="76"/> </region> <region region-id="310" left="6" top="4485" width="147.75" height="36.75" align-x="42.75" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve" subscript="10">p</ml:id> <ml:id xml:space="preserve" subscript="20">p</ml:id> </ml:matrix> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve" subscript="0">α</ml:id> <ml:id xml:space="preserve" subscript="0">β</ml:id> </ml:matrix> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:real>0.3381817820345262</ml:real> <ml:real>0.38124781233483812</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="311" left="342" top="4497" width="56.25" height="16.5" align-x="364.5" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="10">p</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.3381817820345262</ml:real> </result> </ml:eval> </math> <rendering item-idref="78"/> </region> <region region-id="312" left="498" top="4497" width="56.25" height="16.5" align-x="520.5" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="20">p</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.38124781233483812</ml:real> </result> </ml:eval> </math> <rendering item-idref="79"/> </region> <region region-id="326" left="6" top="4583.25" width="88.5" height="15.75" align-x="6" align-y="4596" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Per le velocità:</p> </text> </region> <region region-id="673" left="6" top="4605.75" width="88.5" height="25.5" align-x="36" align-y="4626" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" font="17">p'</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve" font="17">x'</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="80"/> </region> <region region-id="318" left="6" top="4647" width="157.5" height="36.75" align-x="45" align-y="4668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve" subscript="10">p'</ml:id> <ml:id xml:space="preserve" subscript="20">p'</ml:id> </ml:matrix> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" font="17">Φ</ml:id> <ml:real>-1</ml:real> </ml:apply> <ml:matrix rows="2" cols="1"> <ml:id xml:space="preserve" subscript="0">α'</ml:id> <ml:id xml:space="preserve" subscript="0">β'</ml:id> </ml:matrix> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:real>2.8844986402102353</ml:real> <ml:real>-5.4784731079585773</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="319" left="342" top="4659" width="58.5" height="16.5" align-x="366.75" align-y="4668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="10">p'</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2.8844986402102353</ml:real> </result> </ml:eval> </math> <rendering item-idref="82"/> </region> <region region-id="320" left="498" top="4659" width="63.75" height="16.5" align-x="522.75" align-y="4668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="20">p'</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-5.4784731079585773</ml:real> </result> </ml:eval> </math> <rendering item-idref="83"/> </region> <region region-id="343" left="6" top="4727.25" width="219" height="15.75" align-x="42" align-y="4740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Imponendo le condizioni iniziali si ha:</p> </text> </region> <region region-id="674" left="6" top="4758.75" width="116.25" height="46.5" align-x="97.5" align-y="4782" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="1">p</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">A</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="10">p</ml:id> </ml:apply> </math> <rendering item-idref="84"/> </region> <region region-id="675" left="288" top="4769.25" width="39.75" height="15.75" align-x="308.25" align-y="4782" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">quindi </p> </text> </region> <region region-id="676" left="414" top="4758.75" width="120.75" height="46.5" align-x="432.75" align-y="4782" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">A</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="10">p</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.38091449488690149</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="677" left="6" top="4824.75" width="116.25" height="46.5" align-x="97.5" align-y="4848" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="2">p</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">A</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="20">p</ml:id> </ml:apply> </math> <rendering item-idref="86"/> </region> <region region-id="678" left="288" top="4835.25" width="39.75" height="15.75" align-x="308.25" align-y="4848" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">quindi </p> </text> </region> <region region-id="679" left="414" top="4824.75" width="126" height="46.5" align-x="432.75" align-y="4848" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">A</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="20">p</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-1.0617780462276532</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="680" left="6" top="4899" width="96.75" height="18" align-x="75.75" align-y="4908" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="1">p'</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="1">B</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="10">p'</ml:id> </ml:apply> </math> <rendering item-idref="88"/> </region> <region region-id="681" left="288" top="4895.25" width="39.75" height="15.75" align-x="308.25" align-y="4908" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">quindi </p> </text> </region> <region region-id="682" left="414" top="4888.5" width="87.75" height="36.75" align-x="432.75" align-y="4908" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">B</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="10">p'</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.2255603810071386</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="683" left="6" top="4947" width="96.75" height="18" align-x="75.75" align-y="4956" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0ff" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="2">p'</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">B</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="20">p'</ml:id> </ml:apply> </math> <rendering item-idref="90"/> </region> <region region-id="684" left="288" top="4943.25" width="39.75" height="15.75" align-x="308.25" align-y="4956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">quindi </p> </text> </region> <region region-id="685" left="414" top="4936.5" width="93" height="36.75" align-x="432.75" align-y="4956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">B</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="20">p'</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.87509693424591573</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="385" left="6" top="4997.25" width="651" height="19.5" align-x="15" align-y="5010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">La soluzione in coordinate principali è ora calcolabile, perché sono state determinate le costanti A<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>1</sub> </c> </inlineAttr> </f>, B<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>1</sub> </c> </inlineAttr> </f>, A<f family="Arial" charset="0" size="14"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub>2</sub> </c> </inlineAttr> </f>, B<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#f00"> <sub> <f family="Arial" charset="0" size="14">2</f> </sub> </c> </inlineAttr> </p> </text> </region> <region region-id="691" left="6" top="5040.75" width="195" height="46.5" align-x="36" align-y="5064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="386" left="6" top="5112.75" width="195" height="46.5" align-x="36" align-y="5136" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" font="17">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="387" left="6" top="5195.25" width="572.25" height="15.75" align-x="31.5" align-y="5208" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Occorre infine applicare la formula 5.195 per calcolare la soluzione nelle coordinate fisiche α e β</p> </text> </region> <region region-id="392" left="6" top="5229" width="70.5" height="36.75" align-x="32.25" align-y="5250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" font="17">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="2" cols="1"> <ml:apply> <ml:id xml:space="preserve" subscript="1">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> 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optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">α</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" font="17">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="96"/> </region> <region region-id="399" left="6" top="5379.75" width="57" height="20.25" align-x="31.5" align-y="5394" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">β</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" font="17">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="97"/> </region> <region region-id="558" left="6" top="5427" width="41.25" height="16.5" align-x="34.5" align-y="5436" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">T</ml:id> <ml:real>9</ml:real> </ml:define> </math> <rendering item-idref="98"/> </region> <region region-id="559" left="6" top="5463" width="48.75" height="18.75" align-x="25.5" align-y="5478" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Δt</ml:id> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="99"/> </region> <region region-id="485" left="6" top="5517" width="69.75" height="16.5" align-x="16.5" align-y="5526" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">t</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">Δt</ml:id> </ml:sequence> <ml:id xml:space="preserve" subscript="max">T</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="100"/> </region> <region region-id="416" left="6" top="5676" width="763.5" height="266.25" align-x="6" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="101"/> <rendering item-idref="102"/> </region> <region region-id="520" left="6" top="5958" width="758.25" height="266.25" align-x="6" align-y="5958" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="103"/> <rendering item-idref="104"/> </region> <region region-id="213" left="6" top="6281.25" width="300" height="15.75" align-x="21" align-y="6294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Verifica dei calcoli mediante integrazione numerica</p> </text> </region> <region region-id="457" left="6" top="6330.75" width="110.25" height="29.25" align-x="18" align-y="6348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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<ml:id xml:space="preserve" font="17">O</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve" font="17">I</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="2"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </ml:provenance> </math> <rendering item-idref="106"> <element-image-map> <box left="1.5" top="0.75" width="84.75" height="27.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="597" left="150" top="6371.25" width="147.75" height="15.75" align-x="175.5" align-y="6384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" 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