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Equation of motion in tensorial form (relativistic)

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data
    How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge [itex]e[/itex] and mass [itex]m[/itex], with 4-momentum [itex]p^a[/itex] and electromagnetic field tensor [itex]F_{ab}[/itex] of a constant magetic field [itex]\vec B[/itex] perpendicular to the plane of motion. [tex]\frac{dp^a}{d\tau}=\frac{e}{m}F^a{}_bp^b[/tex]
    ?
    Let the the initial condition be [tex]p^a=(E_0 ,\vec 0)[/tex]



    2. Relevant equations
    [tex]\frac{dp^a}{d\tau}=\frac{e}{m}F^a{}_bp^b[/tex]


    3. The attempt at a solution
    I can see that the differential equation resembles that of a SHM equation or a cosh, sinh one if it's a scalar equation. However, I don't know how to deal with a tensor equation. Could anyone please explain? Thank you.
     
  2. jcsd
  3. May 8, 2013 #2
    This is a set of 4 simultaneous linear first order ordinary differential equations in 4 unknowns. Do you know how to solve such a set of equations?
     
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