Birkhoffian formulations of nonholonomic constrained systems

Only for some special nonholonomic constrained systems can a canonical Hami ltonian structure be realized. Based on a reduction of a nonholonomic syste m to a conditional holonomic system, a universal symplectic structure for a constrained system can be constructed in the framework of Birkhoffian gene ralization of Hamiltonian mechanics, which preserves symbiotic character am ong derivability from a variational principle, Lie algebra and symplectic g eometry. Two examples are presented.