The position of a Massless particle is given by:

where v is a user-defined velocity vector.

When the Newtonian, Lagrangian, or Massless formulations are used there are degrees of freedom for the particle position only. When the Newtonian, first order formulation is used there are degrees of freedom for the particle position and velocity. When the Hamiltonian formulation is used, there are degrees of freedom for the particle position and momentum.