The invariant representation of generalized momentum

The relativistic-invariance representation of generalized momentum of a particle in the external field is proposed. In this representation the dependence of potentials of the particle-field interaction on the particle velocity is taken into account. An exact correspondence of expressions for the energy and potential energy for the classical Hamiltonian is established, which makes identical the solutions of problems of mechanics with relativistic and classical approaches. The invariance of the generalized momentum representation allows one to describe equivalently a physical system in geometrically conjugated spaces of kinematical and dynamical variables.