Sometimes it is more convenient to describe the particle motion using a Hamiltonian formulation. In this case, the following system of first-order ODEs is solved:

The particle velocity vH (SI unit: m/s) and particle force FH (SI unit: N) can be entered directly, or, more conveniently by specifying the Hamiltonian, H (SI unit: J). The Hamiltonian is related to the particle velocity and force via the coupled equations

For a more in-depth example, see Choosing a Formulation in the Particle Tracing Modeling chapter.