A geometric setting for generally nonconservative mechanical systems on fibred manifolds is proposed. Emphasis is put on an explicit formulation of nonholonomic mechanics when an unconstrained Lagrangian system moves ...A geometric setting for generally nonconservative mechanical systems on fibred manifolds is proposed. Emphasis is put on an explicit formulation of nonholonomic mechanics when an unconstrained Lagrangian system moves in a generally non-potential force field depending on time, positions and velocities, and the constraints are nonholonomic, not necessarily linear in velocities. Equations of motion, and the corresponding Harniltonian equations in intrinsic form are given. Regularity conditions are found and a nonholonomic Legendre transformation is proposed, leading to a canonical form of the nonholonomic Hamiltonian equations for nonconservative systems.展开更多
基金supported by the Czech Science Foundation (Grant No.GA CˇR 201/09/0981)the Czech-Hungarian Cooperation Programme "Kontakt" (Grant No. MEB041005)the IRSES project ’GEOMECH’ (Grant No. 246981) within the 7th European Community Framework Programme
文摘A geometric setting for generally nonconservative mechanical systems on fibred manifolds is proposed. Emphasis is put on an explicit formulation of nonholonomic mechanics when an unconstrained Lagrangian system moves in a generally non-potential force field depending on time, positions and velocities, and the constraints are nonholonomic, not necessarily linear in velocities. Equations of motion, and the corresponding Harniltonian equations in intrinsic form are given. Regularity conditions are found and a nonholonomic Legendre transformation is proposed, leading to a canonical form of the nonholonomic Hamiltonian equations for nonconservative systems.
