On the forces generated by force fields as a result of interaction between mechanical systems due to superimposed constraints

The motion of a holonomic mechanical system with many degrees of freedom exposed to potential and vortex force fields is considered. The Riemannian space, expanded by two units, is introduced, similar to the space with torsion, in which the motion of the same mechanical system is studied in the absence of force fields, but interacting with another mechanical system moving in the expanded space. The interaction between mechanical systems is taken into account by the dependence of the inertial coefficients of the additional system on the coordinates of the original one. The equations of both holonomic and non-holonomic constraints are determined, which are superimposed on the motion of the initial but free mechanical system in an expanded space and ensure the identity of motion under the action of potential and vortex forces in the initial space. As an example, the motion of a charged material particle in both electromagnetic and gravitational fields is considered.