Introduction to classical mechanics of systems with constraints. Pt.1

Classical theory of mechanical systems with constraints is consistently considered. The following problems are treated in this paper. Lagrangian equations are derived. The connection of symmetry transformations with conserved quantities is demonstrated. Lagrangian and Hamilton's equations of motion for the system with nondegenerate Lagrangians are proved to be equivalent. Restrictions for the choice of noncanonical coordinates in the extended phase space are studied. One-parameter groups of time-dependent canonical transformations are considered