Zakharin S. Variational method for investigation of Lagrangian systems' quasiperiodic solutions

Investigation object: quasiperiodic solutions of Lagrangian systems Investigation purpose: grounding the variational method for finding the quasiperiodic solutions of Lagrangian systems. Investigation methods: averaging method, variational method. Theoretical and practical results, novelty: Existence theorem is proven for classical quasiperiodic solution of generic Lagrangian system without ties with convex on compact set force function. Existence theorem is proven for classical quasiperiodic solution of Lagrangian system with holonomic tie in the form of Riemannian manifold of non-positive curvature. Variational method is grounded for finding the classical quasiperiodic solutions of Lagrangian systems with holonomic ties in the form of complete Riemannian manifolds. Degree of application: it is planned. Sphere (area) of application: nonlinear oscillations theory, classical mechanics