Motion of a Particle in a Penning Trap, parameters and solutions

Ideal equations for motion of a charged particle in a Penning Trap are:

$$ x(t) = rho_{+}cos(omega_{+}t + phi_{+}) + rho_{-}cos(omega_{-}t + phi_{-}) $$
$$ y(t) = (frac{q}{lvert qrvert }) [rho_{+}sin(omega_{+}t + phi_{+}) + rho_{-}sin(omega_{-}t + phi_{-})] $$
$$ z(t) = rho_{z}cos(omega_{z}t + phi_{z}) $$

where,

$$ rho_{+}^2 = frac{2E_{+}}{m(omega_{+}^2 – frac{omega_{z}^2}{2})} d^2 $$
$$ rho_{-}^2 = frac{2E_{-}}{m(omega_{-}^2 – frac{omega_{z}^2}{2})} d^2 $$
$$ rho_{z}^2 = frac{E_{z}}{qU} d^2 $$

and $$ d^2 = frac{1}{4} (2z_{0}^2 + rho_{0}^2) $$ ,
$$ z_{0} , rho_{0} text{ are axial and radial constraints} $$

$$ E_{+},E_{-},E_{z} text{ are kinetic Energies.} $$

$$ text{ I assume } E_{z} = frac{1}{2}mv_{z0}^2, v_{z0} text{ being initial velocity in z axis. Assuming } E_{+},E_{-} text{ are called cyclotron and magnetron kinetic Energies, }$$ How do I find the Kinetic energies assuming we know the initial velocities in x and y direction?

I have been quickly shifting though books on particle traps with the motive to understand the motion of a charged particle in a Penning Trap given U, B, q, m and initial parameters. Trying to make a simulator with Blender