科研之友
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摘要
For the Chaplygin's nonholonomic constrained systems, the constraint manifold can be endowed with Riemann-Cartan geometric structure by nonholonomic mapping into a Riemann manifold. The two kinds of existing dynamics, nonholonomic dynamics and vakonomic dynamics, are compared in the framework of Riemann-Cartan geometry. It is proved that the equations of motion for nonholonomic and vakonomic dynamics are described by the equations of autoparallel and geodesic trajectories on the Riemann-Cartan constraint manifold, respectively. If the metricity condition of Riemann-Cartan connection is satisfied, the torsion (contorsion) of the Riemann-Cartan manifold characterizes the difference between the autoparallel and geodesic trajectories as well as the distinction between the nonholonomic and vakonomic equations.
