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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Calcolo dei fattori di smorzamento modali e delle corrispondenti pulsazioni proprie smorzate</p>
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				<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 smorzati):</p>
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										<ml:id xml:space="preserve" subscript="2">B</ml:id>
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						<ml:apply>
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								<ml:id xml:space="preserve" font="17">Q</ml:id>
								<ml:real>2</ml:real>
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				<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):</p>
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												<ml:id xml:space="preserve">ω</ml:id>
												<ml:real>1</ml:real>
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										</ml:apply>
										<ml:id xml:space="preserve">t</ml:id>
									</ml:apply>
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										<ml:minus/>
										<ml:apply>
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										<ml:apply>
											<ml:mult/>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="1">A</ml:id>
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											</ml:apply>
											<ml:apply>
												<ml:indexer/>
												<ml:id xml:space="preserve">ω</ml:id>
												<ml:real>1</ml:real>
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										</ml:apply>
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							</ml:apply>
							<ml:apply>
								<ml:id xml:space="preserve">cos</ml:id>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve" subscript="s1">ω</ml:id>
									<ml:id xml:space="preserve">t</ml:id>
								</ml:apply>
							</ml:apply>
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			<math optimize="false" disable-calc="false">
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													<ml:apply>
														<ml:indexer/>
														<ml:id xml:space="preserve">ω</ml:id>
														<ml:real>2</ml:real>
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						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:apply>
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										<ml:apply>
											<ml:mult/>
											<ml:apply>
												<ml:mult/>
												<ml:id xml:space="preserve" subscript="2">A</ml:id>
												<ml:id xml:space="preserve" subscript="2">ξ</ml:id>
											</ml:apply>
											<ml:apply>
												<ml:indexer/>
												<ml:id xml:space="preserve">ω</ml:id>
												<ml:real>2</ml:real>
											</ml:apply>
										</ml:apply>
									</ml:apply>
								</ml:parens>
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							<ml:apply>
								<ml:id xml:space="preserve">cos</ml:id>
								<ml:apply>
									<ml:mult/>
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									<ml:id xml:space="preserve">t</ml:id>
								</ml:apply>
							</ml:apply>
						</ml:apply>
					</ml:apply>
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			<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="264" left="6" top="3617.25" width="746.25" height="47.25" align-x="13.5" align-y="3630" 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>
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			<math optimize="false" disable-calc="false">
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					<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="76"/>
		</region>
		<region region-id="271" left="210" top="3701.25" width="89.25" height="15.75" align-x="221.25" align-y="3714" 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="269" left="6" top="3747.75" width="87" height="25.5" align-x="35.25" align-y="3768" 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="77"/>
		</region>
		<region region-id="273" left="210" top="3755.25" width="83.25" height="15.75" align-x="221.25" align-y="3768" 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="3815.25" width="171" height="15.75" align-x="6" align-y="3828" 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>
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						<ml:apply>
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						<ml:apply>
							<ml:id xml:space="preserve" font="17">x</ml:id>
							<ml:real>0</ml:real>
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					</ml:apply>
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			</math>
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			<math optimize="false" disable-calc="false">
				<ml:apply xmlns:ml="http://schemas.mathsoft.com/math30">
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					<ml:apply>
						<ml:id xml:space="preserve" font="17">p'</ml:id>
						<ml:real>0</ml:real>
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					<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>
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		</region>
		<region region-id="293" left="6" top="3959.25" width="330.75" height="15.75" align-x="6" align-y="3972" 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>
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						<ml:id xml:space="preserve" font="17">x</ml:id>
						<ml:real>0</ml:real>
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					<ml:matrix rows="2" cols="1">
						<ml:id xml:space="preserve" subscript="0">α</ml:id>
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			<math optimize="false" disable-calc="false">
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						<ml:real>0</ml:real>
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						<ml:id xml:space="preserve" subscript="0">α'</ml:id>
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			<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">
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							<ml:mult/>
							<ml:real>20</ml:real>
							<ml:id xml:space="preserve">deg</ml:id>
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							<ml:id xml:space="preserve">rad</ml:id>
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						<result xmlns="http://schemas.mathsoft.com/math30">
							<unitedValue>
								<ml:real>0.3490658503988659</ml:real>
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				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
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							<ml:mult/>
							<ml:real>10</ml:real>
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								<ml:real>0.17453292519943295</ml:real>
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			<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="84"/>
		</region>
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			<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="85"/>
		</region>
		<region region-id="322" left="6" top="4187.25" width="348.75" height="15.75" align-x="6" align-y="4200" 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="4229.25" width="94.5" height="15.75" align-x="17.25" align-y="4242" 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>
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			<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>
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				<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>
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				<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>
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				<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>
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