Particle Moving Along y Axis on Surface of Rotating Ellipse

Suppose an ellipse with one focus at the origin is made to rotates about the origin in the  
\[xy\]
  plane. A particle on the surface of the ellipse is made to move as the ellipse rotates. What will be the velocity and acceleration of the particle?
(P ALIGN="CENTER">rotting ellipse

If the minor and major axes have length  
\[b, \; a\]
  respectively, the coordinates of a point on the surface of the ellipse with origin at one focus is  
\[(r, \theta )\]
  in polar coordinates with  
\[r= \frac{b^2}{a(1- ecos \theta )}\]
  and the velocity is  
\[\frac{dr}{dt}= - \frac{eb^2 \dot{\theta} sin \theta }{a(1-e cos \theta )^2} \]
.
The acceleration is  
\[\frac{d^2r}{dt^2}= - \frac{eb^2 (\ddot{\theta} sin \theta + \dot{\theta}^2 cos \theta )}{a(1-e cos \theta )^2} - \frac{2e^2b^2 (\dot{\theta}^2 sin^2 \theta}{a(1-e cos \theta )^3} \]
.

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