  New, gauge-independent, second-order Lagrangian for the motion of classical,
charged test particles is used to derive the corresponding Hamiltonian
formulation. For this purpose a Hamiltonian description of the theories derived
from the second-order Lagrangian is presented. Unlike in the standard approach,
the canonical momenta arising here are explicitely gauge-invariant and have a
clear physical intepretation. The reduced symplectic form is equaivalent to the
Souriau's form. This approach illustrates a new method of deriving equations of
motion from field equations.
