Hamiltonian formalism for Lagrangian systems with assigned connection

The method of constructing the canonical formalism, proposed by F.A. Berezin, is developed and applied to a number of the Lagrangian systems with the assigned connections, depending on the velocities. The method is applicable both for the nondegenerated and degenerated Lagrangians and it is based on the introduction of the generalized Lagrangian function, including the Lagrangian multipliers of the connections equations and building therewith the generalized pulses. The basic idea of the method consists in consideration of the joined system of equations for the generalized pulses and connections, wherefrom all the velocities are expressed through these pulses and coordinates. The nondegeneration or degeneration of such a system is determined not through the initial Lagrangian but through the possibility of the unambiguous consideration of this connection relative to the velocities. The canonical formalism is plotted for the nondegenerated mechanical connection with the holonomic connection, for the Lagrangian function, linear one by the velocities, as well as for the material relativistic particle by the proper time calibration and for the relativistic string with the Lagrangian connections, depending on the velocities. The application of the above method for the vector massive field and the electromagnetic field with the Lorentz condition leads to the known results but through the algorithmically uniform approach