1. Dec 30, 2012

### Horv

Hi all!

So if I had any kind of field for example $\bar{F}(x,y) = (0,x)$ wich represents a river or somthing similar and I put into the river a particle, or point-like body how can I get the path, or curve (flwo line?) from the vector field? I mean that path which the particle or the body moves.

Last edited: Dec 30, 2012
2. Dec 30, 2012

### HallsofIvy

What vector field does that represent? The force vector (which would give acceleration) or the velocity vector? If the velocity vector, then it represents the two equations dx/dt= 0 and dy/dt= x. That is a system of differential equations and there are several ways of solving that system.

The simplest way would be to first differentiate both sides of dy/dt= x with respect to t: $d^2y/dt^2= dx/dt= 0$ so that y(t)= At+ B for any constants A and B. And then x(t)= dy/dt= A.