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- Homework Statement
- Show that a point with acceleration given by:

a=c*((dr/dt)×r)/|r|3

where c is a constant, moves on the surface of a cone.

- Relevant Equations
- v=dr/dt

This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that there is an constat vector 'a' that satisfy a•r=constant, than the motion would be on the surface of a cone. So i tried to make use of some vectorial identity multiplying by cross product on both sides and try to use the 'BAC-CAB' rule, but that didnt lead to anywhere.

Is there any example similar to this case or anywhere i can study to have a better understanding?

Is there any example similar to this case or anywhere i can study to have a better understanding?