Geometric mechanics: Foundations of the theory and fundamental equations

Geometric mechanics, which develops traditional geometric methods of mechanics, enables one to construct theories of complex coupled systems on the basis of Newtonian axiomatics without recourse to the methods of Lagrangian analytical mechanics, Euler's methods for the dynamics of a rigid body and other theories and principles. Geometric methods simplify the general theory of complex mechanical systems and bring it closer to computerized computational technologies and to engineering practice.