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Why is phase space important? As far as I'm concerned, you're just rewriting the dynamic law using momentum instead of velocity and mass. $$m \space \frac {d \ \vec v}{d\ t}=\vec F \\ \frac{d \ \vec r}{d \ t} = \vec v$$ Changed to $$ \frac {d \ \vec p} {d \ t} = \vec F \\ \frac {d \ \vec r}{d \ t} = \frac {\vec p}{m}$$

Qmechanic
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Eric Zhang
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    Liouville’s theorem https://en.m.wikipedia.org/wiki/Liouville%27s_theorem_(Hamiltonian) and canonical transformations https://en.wikipedia.org/wiki/Canonical_transformation come to mind – ZeroTheHero May 10 '18 at 02:20
  • It is a formulation consistent with special relativity vectors – anna v May 10 '18 at 03:54
  • Possible duplicates: https://physics.stackexchange.com/q/89035/2451 and links therein. – Qmechanic May 10 '18 at 05:06

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Define phase space:

In mathematics and physics, a phase space of a dynamical system is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.

So you mean why chose momentum and position? For conceptual and mathematical simplicity. In addition this carries over when special relativity is included with its four vectors ${(t,x,y,z)}$ and ${(E,p_x,p_y,p_z)}$

anna v
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