1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted