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Finding a solution for Relativistic Acceleration

  1. Jun 8, 2012 #1
    I tried all my mathcad software such as Maple and I can't seem to find a solution to this time based differential equation.

    m}\left%20(%201%20-%20\frac{\left%20[%20f(t)%20\right%20]^{2}}{c^{2}}%20\right%20)^{\frac{3}{2}}.gif
     
  2. jcsd
  3. Jun 8, 2012 #2
    Hi !

    Very surprising ! They should solve this EDO without any difficulty, since it is an EDO of the "separable variables" kind. This can be handly carried out.
     
  4. Jun 8, 2012 #3
    Whenever you have a messy-looking equation, it's sometimes helpful to at least initially, get rid of all the fluff by canonicalizing the equation. In the case above, write it simply as:

    [tex]\frac{dy}{dt}=k(1-y^2/a)^{3/2}[/tex]

    See, just that lil' bit is good progress. Now, you can't separate variables and integrate? Telll you what, can you integrate just:

    [tex]\int \frac{dy}{(1-y^2/a)^{3/2}}[/tex]

    I haven't tried so I don't know. You try it.
     
    Last edited: Jun 8, 2012
  5. Jun 8, 2012 #4

    hunt_mat

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    This might be a two stage process, first try a substitution of [itex]y=\sqrt{a}\sin\theta[/itex] and see what you get.
     
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