# Why is dynamics first order in phase space?

I have watched some lectures in which the lecturer said that system dynamics are (generally?) first order in phase space, forming a system of coupled differential equations. At a basic level I see this as reflecting Newton's second law $\frac{\partial ^2 x}{\partial t^2}=\frac{\partial p}{\partial t}/m$, however it is not at all clear to me that this is general (if it is).

• Which lectures? – Qmechanic Aug 4 '18 at 13:55