Velocity as a function of radial distance on an elliptical trajectory

AI Thread Summary
The discussion focuses on determining the velocity W(m) of a point on an ellipse described by the vector r=m(a cos(θ), b sin(θ)), where m varies from 0 to 1. Participants explore whether angular velocity remains constant in elliptical motion, contrasting it with circular motion. The importance of taking the time derivative of the position vector and calculating the magnitude of dr/dt is emphasized for finding the velocity. The relationship between radial distance and velocity on an elliptical trajectory is examined, highlighting the complexities compared to circular paths. The conversation underscores the need for careful mathematical analysis in understanding motion on elliptical trajectories.
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Homework Statement



Assume that a point on an ellipse is described by the vector r=m(a\cos{\theta},b\sin{\theta}), where 0\leq m\leq 1 and that the vector is rotating in the clockwise direction at constant tangential velocity W when m=1.

The problem is to find the velocity W(m).

Also, is the angular velocity constant as it is for circular motion?
 
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Did you take the time derivative of it and then calculate the magnitude of dr/dt?
 

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