# Equation of motion in tensorial form (relativistic)

1. May 8, 2013

### vidi

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 $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant magetic field $\vec B$ perpendicular to the plane of motion. $$\frac{dp^a}{d\tau}=\frac{e}{m}F^a{}_bp^b$$
?
Let the the initial condition be $$p^a=(E_0 ,\vec 0)$$

2. Relevant equations
$$\frac{dp^a}{d\tau}=\frac{e}{m}F^a{}_bp^b$$

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. May 8, 2013

### Staff: Mentor

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?