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Integrating equations of motion

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose that the force acting on a particle is factorable into the following forms.

    (a) F (x,t) = f(x)g(t)
    (b) F (v, t) = f(v)g(t)
    (c) F (x, v) = f(x) g(v)

    For which of these cases are the equations of motion integrable


    2. Relevant equations

    F = md2x / dt2

    3. The attempt at a solution

    I just need to check whether I am on the right track

    What I did was take F = mdv/dt and used the chain rule ( F = dv/dt = dv/dx times dx/dt = v(dv/dx = F).

    So since F = v*(dv/dx), and for (a), F is a function of t, it is impossible to separate and integrate the equations of motion?

    For (b) it is impossible to integrate the equations of motion because there is again a time variable in F

    For (c), it is possible to integrate equations of motion because F is a function of x and v and you can easily separate and integrate equations of motion using F = v*(dv/dx).
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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