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Mecánica - Cambios recientes [es]
2026-07-20T07:53:22Z
Realiza un seguimiento de los cambios más recientes en la wiki en este canal.
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https://mec.etseib.upc.edu/es/index.php?title=D8._Conservaciones&diff=821&oldid=534
D8. Conservaciones
2026-07-15T11:48:02Z
<p><span dir="auto"><span class="autocomment">✏️ EJEMPLO D8.8: barra dentro de guía lisa circular giratoria</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisión anterior</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisión del 11:48 15 jul 2026</td>
</tr><tr><td colspan="4" class="diff-multi" lang="es">(No se muestra una edición intermedia del mismo usuario)</td></tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l517">Línea 517:</td>
<td colspan="2" class="diff-lineno">Línea 517:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>\braq{\overline{\Hs}_\mathrm{RTO}(\Os)}{}=\left(\ms<del style="font-weight: bold; text-decoration: none;">(\sqrt{3</del>\rs<del style="font-weight: bold; text-decoration: none;">})</del>^2\diag{1}{0}{1}+\ms\left(\frac{\rs}{2}\right)^2\diag{1}{1}{0}\right)\vector{\dot{\theta}}{\dot{\psi}\sin\theta}{\dot{\psi}\cos\theta}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>\braq{\overline{\Hs}_\mathrm{RTO}(\Os)}{}=\left(<ins style="font-weight: bold; text-decoration: none;">\frac{1}{4}</ins>\ms\rs^2\diag{1}{0}{1}+\ms\left(\frac{\rs}{2}\right)^2\diag{1}{1}{0}\right)\vector{\dot{\theta}}{\dot{\psi}\sin\theta}{\dot{\psi}\cos\theta}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>\braq{\overline{\Hs}_\mathrm{RTO}(\Os)}{}=\frac{1}{4}\ms\rs^2\vector{<del style="font-weight: bold; text-decoration: none;">14</del>\dot{\theta}}{\dot{\psi}\sin\theta}{<del style="font-weight: bold; text-decoration: none;">13</del>\dot{\psi}\cos\theta}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>\braq{\overline{\Hs}_\mathrm{RTO}(\Os)}{}=\frac{1}{4}\ms\rs^2\vector{<ins style="font-weight: bold; text-decoration: none;">2</ins>\dot{\theta}}{\dot{\psi}\sin\theta}{\dot{\psi}\cos\theta}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_\mathrm{vert} =\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_3\cos\theta+ \left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_2\sin\theta= \frac{1}{4}\ms\rs^2\dot{\psi}<del style="font-weight: bold; text-decoration: none;">(13</del>\cos^2\theta + \sin^2\theta)= \frac{1}{4}\ms\rs^2 \dot{\psi}<del style="font-weight: bold; text-decoration: none;">(1+12\cos^2\theta)</del></math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_\mathrm{vert} =\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_3\cos\theta+ \left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_2\sin\theta= \frac{1}{4}\ms\rs^2<ins style="font-weight: bold; text-decoration: none;">(</ins>\dot{\psi}\cos^2\theta + <ins style="font-weight: bold; text-decoration: none;">\dot{\psi}</ins>\sin^2\theta)= \frac{1}{4}\ms\rs^2 \dot{\psi}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_\mathrm{vert} =\text{<del style="font-weight: bold; text-decoration: none;">constant </del> } \Rightarrow \quad \frac{\ds\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_\mathrm{vert}}{\ds\ts}=0=\frac{1}{4}\ms\rs^2 \<del style="font-weight: bold; text-decoration: none;">dot</del>{\psi}<del style="font-weight: bold; text-decoration: none;">(1+12\cos^2\theta)-6\ms\rs^2 \dot{\psi}\dot{\theta}\sin\theta\cos\theta </del></math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_\mathrm{vert} =\text{<ins style="font-weight: bold; text-decoration: none;">constante </ins> } \Rightarrow \quad \frac{\ds\left.\overline{\Hs}_\mathrm{RTO}(\Os)\right]_\mathrm{vert}}{\ds\ts}=0=\frac{1}{4}\ms\rs^2 \<ins style="font-weight: bold; text-decoration: none;">ddot</ins>{\psi} </math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>\boxed{\ddot{\psi}<del style="font-weight: bold; text-decoration: none;">(3+7\cos^2\theta)-14\dot{\psi}\dot{\theta} \sin\theta \cos\theta </del>=0}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>\boxed{\ddot{\psi}=0}</math></div></td></tr>
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Eantem
https://mec.etseib.upc.edu/es/index.php?title=D7._Ejemplos_de_din%C3%A1mica_3D&diff=819&oldid=815
D7. Ejemplos de dinámica 3D
2026-07-15T11:11:30Z
<p><span dir="auto"><span class="autocomment">✏️ EJEMPLO D7.5: anilla giratoria</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisión anterior</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisión del 11:11 15 jul 2026</td>
</tr><tr><td colspan="4" class="diff-multi" lang="es">(No se muestra una edición intermedia del mismo usuario)</td></tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l108">Línea 108:</td>
<td colspan="2" class="diff-lineno">Línea 108:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==D7.1 Análisis de ecuaciones del movimiento==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==D7.1 Análisis de ecuaciones del movimiento==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>La obtención de las ecuaciones del movimiento de los GL libres de los sistemas multisólido no es, en general, el objetivo de los problemas de dinámica, sino un paso previo a su integración para conocer cómo evolucionan a lo largo del tiempo las coordenadas que describen la configuración del sistema:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>La obtención de las ecuaciones del movimiento de los GL <ins style="font-weight: bold; text-decoration: none;">(<math>\dot{\qs}_{i}</math>) </ins>libres de los sistemas multisólido no es, en general, el objetivo de los problemas de dinámica, sino un paso previo a su integración para conocer cómo evolucionan a lo largo del tiempo las coordenadas que describen la configuración del sistema:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>\ddot{\qs}_{i}\xrightarrow[]{\int{\ds\ts}}\dot{\qs}_\is\xrightarrow[]{\int{\ds\ts}}{\qs_\is}</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>\ddot{\qs}_{i}\xrightarrow[]{\int{\ds\ts}}\dot{\qs}_\is\xrightarrow[]{\int{\ds\ts}}{\qs_\is}</math></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l714">Línea 714:</td>
<td colspan="2" class="diff-lineno">Línea 714:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:[[Archivo:D7-Ex5-7-esp.png|thumb|center|450px|link=]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:[[Archivo:D7-Ex5-7-esp.png|thumb|center|450px|link=]]</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center> 5 inc. de restricción + <math>\Gamma = </math> 6 inc.<math>\:\:\:\:\:\:\:\:\:\:</math> 9 inc. de restricción + <math>\Gamma = </math> 10 inc.</center></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:La mejor opción, pues, es aplicar teoremas a la anilla. Las interacciones externas sobre este sólido son:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:La mejor opción, pues, es aplicar teoremas a la anilla. Las interacciones externas sobre este sólido son:</div></td></tr>
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Eantem