View source for Phase velocity vector

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The vector $f(x)$ originating at a point $x$ of the [[Phase space|phase space]] $G$ of the [[Autonomous system|autonomous system]]

$$\dot x=f(x),\quad f\in C^1(G),\quad G\subset\mathbf R^n.$$

Let $\Gamma$ be the [[Phase trajectory|phase trajectory]] of the system passing through a point $\xi\in G$; if $f(\xi)\neq0$, then the phase velocity vector $f(\xi)$ is tangent to $\Gamma$ and represents the instantaneous rate of the motion along $\Gamma$ of a representative point of the system at the moment of passing through the position $\xi\in\Gamma$. If $f(\xi)=0$, then $\xi\in G$ is an [[Equilibrium position|equilibrium position]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  L.S. Pontryagin,   "Ordinary differential equations" , Addison-Wesley  (1962)  (Translated from Russian)</TD></TR></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  V.I. Arnol'd,   "Geometrical methods in the theory of ordinary differential equations" , Springer  (1983)  (Translated from Russian)</TD></TR></table>