Deriving a formula for velocity from the Lagrangian formula for generalized momentum

Asked Aug 12 '20 at 22:15

Active Aug 12 '20 at 22:26

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On pg. 96 of No-Nonsense Classical Mechanics, the author asserts:

The trouble I am having is with the highlighted portions. In particular, how do we derive a general formula for velocity $\dot{q}$:

$$ \dot{q} = \dot{q}(q, p) $$

from the formula for "generalized momentum" in the Lagrangian setting:

$$ p = \frac{\partial L } { \partial \dot{q} } $$

edited Aug 12 '20 at 22:26

Bernard

asked Aug 12 '20 at 22:15

user1770201

1

I guess it means that $p = \frac{\partial L}{\partial \dot{q}} = f(q,\dot{q},t)$. Then we may try to express $\dot{q} = g(p,q,t)$. – openspace Aug 12 '20 at 22:19
Is there a way to determine what $g$ is in general? – user1770201 Aug 12 '20 at 22:44

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