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Integration of motion equation

  1. Jul 28, 2011 #1
    Hi , I am trying to integrate this equation :
    X"(t) = F(t) - 1 where X'(0) = X(0)= 0
    F(t) force of a rocket , 0<t<T

    solution they got : X(T) = [integral 0 to T of { (T-t)F(t)d(t) } ] - [square of T ] / 2
     
  2. jcsd
  3. Jul 29, 2011 #2

    CompuChip

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    If X''(t_0) = F(t_0) - 1, then
    [tex]X'(t_1) = \int_0^{t_1} X''(t_0) \, dt_0[/tex]
    and
    [tex]X(t_2) = \int_0^{t_2} X'(t_1) \, dt_1 = \int_0^{t_2} \int_0^{t_1} X'(t_0) \, dt_0 \, dt_1 [/tex].
     
  4. Jul 29, 2011 #3
    thanks for your reply, what you mean by [tex]
    thanks
     
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