INTRINSIC GEOMETRY OF A DYNAMIC SYSTEM WITH NON-INTEGRABLE LINEAR RELATIONSHIP

The article discusses almost contact metric space endowed with N-extended metric connection, as a manifold configurations of dynamic systems with non-integrable linear connection. We give a geometric description of a dynamic system with non-integrable linear relationship involving the Lagrangian and Hamiltonian formalism. We study the motion of specific dynamical systems for which configuration spaces are special cases of Riemannian manifolds. These manifolds, first of all, should be attributed almost contact metric space with zero curvature distribution. Using Noether's theorem, extended to the case of almost contact spaces, we propose a method of constructing the first integrals nonholonomic Hamiltonian system.