Feng-Xiang Mei

Birkhoffian formulations of nonholonomic constrained systems

Abstract Only for some special nonholonomic constrained systems can a canonical Hamiltonian structure be realized. Based on a reduction of a nonholonomic system to a conditional holonomic system, a universal symplectic structure for a constrained system can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics, which preserves symbiotic character among derivability from a variational principle, Lie algebra and symplectic geometry. Two examples are presented.

Poincare-Cartan Integral Invariants of Nonconservative Dynamical Systems

Traditionally there do not exist integralinvariants for a nonconservative system in the phasespace of the system. For weak nonconservative systems,whose dynamical equations admit adjoint symmetries, there exist Poincare and Poincare-Cartanintegral invariants on an extended phase space, wherethe set of dynamical equations and their adjointequations are canonical. Moreover, integral invariantsalso exist for pseudoconservative dynamical systemsin the original phase space if the adjoint symmetriessatisfy certain condtions.