How to go from the configuration space to the phase space?

1. Aug 18, 2011

aries0152

How can we go from the configuration space of the system to the phase space when velocity can be expressed in terms of momenta?

Last edited: Aug 18, 2011
2. Aug 18, 2011

mathfeel

By a Legrendre transformation. Suppose $f(q, \dot{q})$ is a function of configuration space variable, then there is a corresponding function in phase space is:$g(q, p) = \dot{q}(p) p - f(q, \dot{q}(p))$.