# What is the purpose of phase space? [duplicate]

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 $$\frac {d \ \vec p} {d \ t} = \vec F \\ \frac {d \ \vec r}{d \ t} = \frac {\vec p}{m}$$
## marked as duplicate by Qmechanic♦ classical-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); May 10 '18 at 5:06
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 ${(E,p_x,p_y,p_z)}$