Point Particle in Magnetic Field

[littleHilbert]

Hey, Guys!

Could you please give me some guidance for the following problem:

A point particle of mass m and charge q moves with an arbitrary initial velocity $\vec{v}$ in constant magnetic field $\vec{B}$. The point particle is moving under the influence of the Lorentz-force:$\vec{K}=\frac{q}{c}(\vec{v}\times\vec{B})$, where c - speed of light. Evaluate the path:$\vec{r}(t)$

Where or how should I start? Just ask me guiding questions, please.

Thanks

 

[littleHilbert]

We formulate the law of motion as ODE:
$m\vec{a}=\frac{q}{c}(\vec{v}\times\vec{B})$, where of course $\vec{a}=\ddot\vec{r},\vec{v}=\dot\vec{r}$ So all we have to do is to solve this ODE. But how do we handle the cross-product in an ODE?

 

[antonantal]

I'm not sure but maybe you should write the cross product in the matrix determinant form.