Is there any physical scalar potential where $U$ is also depends on $\dot q_i$s?

Question

In the book of Classical Mechanics by Goldstein, at page 21, while deriving the Lagrange's equation, when the external forces are derivable from a scalar potential $U$, the author implicitly assumes that $U = U(q_i, t)$.

However, is there any physical scalar potential where $U$ is also depends on $\dot q_i$s ?

score 2 · Accepted Answer · answered Feb 15 '19 at 20:28

2

Yes, e.g. the velocity-dependent potentials for the Lorentz force and the Coriolis force. See also e.g. this Phys.SE post.

answered Feb 15 '19 at 20:28

Qmechanic

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Is there any physical scalar potential where $U$ is also depends on $\dot q_i$s?

1 Answers1