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Particle moving in potential.

  1. Aug 14, 2014 #1
    If I have particle moving in the potential ##V(x)##, when I write equation of motion
    ## \frac{dx}{dt}=-V'(x)+q(t)##
    and when I integrate this equation do I need to look ##V'(x)## as function of time, or I just could write
    ## x(t)=-V'(x)t+\int^t_0q(t)dt ##
    Thanks for your answer!
     
  2. jcsd
  3. Aug 14, 2014 #2
    It depends on how V is defined. According to what you wrote V=V(x) is just a function of space and hence you are correct.

    Anyway, what's q(t)? And how did you obtain that equation of motion?
     
  4. Aug 14, 2014 #3
    Yes but ##x=x(t)## and ##V=V(x)##. So I am confused. But because ##V(x)## is potential I think that I write equation in correct form. This is potential in which particle moves.
     
  5. Aug 14, 2014 #4

    ShayanJ

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    It seems you're using kind of a "constant of differentiation"(like a constant of integration) which is mathematically wrong!!!
    You should add a constant only when you integrate something, not when you differentiate something!!!
     
  6. Aug 14, 2014 #5

    Orodruin

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    No, you are not allowed to integrate the equations of motion like that. Even if V does not depend explicitly on time, it does so implicitly through x.

    I also agree with earlier answers that your EoM looks weird.
     
  7. Aug 15, 2014 #6
    Yes but you know. Particle is moving in some potential ##V(x)##. In certain moment ##t## it has coordinate ##x(t)##. ##q(t)## is certain pulse. How do you write down this solution?
     
  8. Aug 15, 2014 #7

    ShayanJ

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    Well...You can't write the solution without knowing what is q(t)!
     
  9. Aug 15, 2014 #8

    ShayanJ

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    Well...You can't write the solution without knowing what is q(t)!

    Also the following is wrong.
    Because x is an unknown function of time so you can't integrate. That's called a differential equation and it has its own methods.
     
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