Canonical Equations of Singular Mechanical Systems in Terms of Quasi-coordinates

The constrained mechanical systems by quasi-coordinates are more universal than by generalized coordinates. In this paper, the motion equations of non-conservative singular mechanical systems by quasi-coordinates in phase space are studied. The regularization forms of Boltzmann-Hamel equations for general holonomic and nonholonomic singular mechanical systems are derived. The results show that the canonical equations expressed by quasi-coordinates and quasi-velocities have a completely single structure, which do not depend on the constraints or not. The nonholonomic singular mechanical system is a natural extension of the general holonomic singular mechanical system.