A Lagrangian formalism based on the velocity-determined virtual displacements for systems with nonholonomic constraints

摘要

We develop a Lagrangian formulation for classical systems with a general nonholonomic constraints by utilizing the so-called velocity-determined virtual-displacement conditions, i.e. by assuming the virtual displacements to be along the direction of the velocities in a special reference frame. It is shown that our general scheme encompasses as special cases the Chetaev and Voronets approaches when the constraints are homogeneous or linear in relative velocities.