Problem: Consider a particle of mass m, constrained to move in a circle of radius r. Find the Lagrangian:(adsbygoogle = window.adsbygoogle || []).push({});

Relevant Equations: L = T - V

Where L is the Lagrangian, T is the kinetic energy, and V is the potential energy.

My questions is this. T is the kinetic energy and would simply equal mV^2/2 or mr^2w^2/2 depending on the coordinate system chosen.

What about V? There has to be a force on the particle holding it in its circular trajectory or it would simply fly off. However, no central force is mentioned in the problem. For all I know the particle may be held in place by a string, or maybe it rides in a circular track. Anyhow, does it make sense to talk about a potential energy associated with centripetal force?

Is it possible that L = T - V doesn't hold in this case since the forces involved are velocity dependent (centripetal force)? I know for the EM Lagrangian L is not T - V.

jsc

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# Uniform Circular Motion in Lagrangian Formalism

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