Phase space. Phase trajectories.

[LagrangeEuler]

If I understand well like in kinematics where we could have eq of motion $x=x(t)$, $y=y(t)$ and we get eq of trajectory with elimination of time. In dynamics we have $x=x(t)$, $p=p(t)$ and with elimination of time we get eq of phase trajectory. Am I right?

 

[Filip Larsen]

If I read your question correct, no. I see no reason why phase space can't be just as relevant for both for a purely kinematic set of equations as for a dynamical problem, even if we mostly use the term phase space in the later situation. For instance, phase space makes perfect sense also for simple mechanical systems which has only kinematic state (like position and velocity).