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Question about Vector Fields

  1. Dec 30, 2012 #1
    Hi all!

    I want to ask about vector fields.
    So if I had any kind of field for example [itex]\bar{F}(x,y) = (0,x)[/itex] 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.

    Thanks for the answers.
     
    Last edited: Dec 30, 2012
  2. jcsd
  3. Dec 30, 2012 #2

    HallsofIvy

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    Staff Emeritus
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    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: [itex]d^2y/dt^2= dx/dt= 0[/itex] so that y(t)= At+ B for any constants A and B. And then x(t)= dy/dt= A.
     
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