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![[parent]](https://images.physicslibrary.org/images/uparrow.png)
spherical coordinate motion example of generalized coordinates
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(Example)
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As an example let us get the equations in spherical coordinates for the motion.
Where
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"spherical coordinate motion example of generalized coordinates" is owned by bloftin.
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This object's parent.
Cross-references: motion
This is version 2 of spherical coordinate motion example of generalized coordinates, born on 2008-07-18, modified 2008-07-21.
Object id is 289, canonical name is SphericalCoordinateMotionExampleOfGeneralizedCoordinates.
Accessed 578 times total.
Classification:
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Pending Errata and Addenda
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![$\displaystyle T=\frac{m}{2}\left[\dot{r}^{2}+ r^2 \dot{\theta}^2 r^2 \sin^{2}\theta\dot{\phi}^{2}\right]. $](http://images.physicslibrary.org/cache/objects/289/l2h/img2.png "$\displaystyle T=\frac{m}{2}\left[\dot{r}^{2}+ r^2 \dot{\theta}^2 r^2 \sin^{2}\theta\dot{\phi}^{2}\right]. $")
![$\displaystyle \frac{\partial T}{\partial r}=m r\left[\dot{\theta}^{2}+\sin^{2}\theta\dot{\phi}^{2}\right], $](http://images.physicslibrary.org/cache/objects/289/l2h/img4.png "$\displaystyle \frac{\partial T}{\partial r}=m r\left[\dot{\theta}^{2}+\sin^{2}\theta\dot{\phi}^{2}\right], $")
![$\displaystyle \delta_{r}W=m\left[\ddot{r}-r\left(\dot{\theta}^{2}+\sin^{2}\theta\dot{\phi}^{2}\right)\right] \delta r=R\delta r, $](http://images.physicslibrary.org/cache/objects/289/l2h/img8.png "$\displaystyle \delta_{r}W=m\left[\ddot{r}-r\left(\dot{\theta}^{2}+\sin^{2}\theta\dot{\phi}^{2}\right)\right] \delta r=R\delta r, $")
![$\displaystyle \delta_{\theta}W=m\left[\frac{d}{dt}\left(r^{2}\dot{\theta}\right... ...\sin\theta\cos\theta\dot{\phi}^{2}\right] \delta\theta=\Theta r \delta \theta, $](http://images.physicslibrary.org/cache/objects/289/l2h/img9.png "$\displaystyle \delta_{\theta}W=m\left[\frac{d}{dt}\left(r^{2}\dot{\theta}\right... ...\sin\theta\cos\theta\dot{\phi}^{2}\right] \delta\theta=\Theta r \delta \theta, $")
![$\displaystyle m \left \{\frac{d^{2}r}{dt^{2}}-r\left[\left(\frac{d\theta}{dt}\right)^{2}+\sin^{2}\theta\left(\frac{d\phi}{dt}\right)^{2}\right]\right\}=R, $](http://images.physicslibrary.org/cache/objects/289/l2h/img11.png "$\displaystyle m \left \{\frac{d^{2}r}{dt^{2}}-r\left[\left(\frac{d\theta}{dt}\right)^{2}+\sin^{2}\theta\left(\frac{d\phi}{dt}\right)^{2}\right]\right\}=R, $")
![$\displaystyle \frac{m}{r}\left[\frac{d}{dt}\left(r^{2}\frac{d\theta}{dt}\right)-r^{2}\sin\theta\cos\theta\left(\frac{d\phi}{dt}\right)^2\right]=\Theta, $](http://images.physicslibrary.org/cache/objects/289/l2h/img12.png "$\displaystyle \frac{m}{r}\left[\frac{d}{dt}\left(r^{2}\frac{d\theta}{dt}\right)-r^{2}\sin\theta\cos\theta\left(\frac{d\phi}{dt}\right)^2\right]=\Theta, $")
