integral curve

Definition Suppose M is a smooth manifoldMathworldPlanetmath, and X is a smooth vector field on M. Then an integral curve of X through a point xM is a curve c:IM, such that

c(t) = (Xc)(t),for all t in I
c(0) = x.

Here I is some open interval of 0, and c(t) is the tangent vector in Tc(t)M represented by the curve.

Suppose xi are local coordinates for M, ci are functionsMathworldPlanetmath representing c in these local coordinates, and X=Xixi. Then the condition on c is

dcidt(t)=Xic(t),for all t.
Title integral curve
Canonical name IntegralCurve
Date of creation 2013-03-22 15:16:31
Last modified on 2013-03-22 15:16:31
Owner matte (1858)
Last modified by matte (1858)
Numerical id 5
Author matte (1858)
Entry type Definition
Classification msc 53-00