Reduced equations for nonholonomic mechanical systems with dissipative forces
The main topic of the paper is the problem of computing reduced equation for mechanical systems both in the constrained (mixed kinematic and dynamic) and unconstrained case. In the latter one the structure of the reduced Lagrangian reveals the local forms of the locked inertia tensor and the mechanical connection, both useful components in the reduction process. This structure is surprisingly simple and can be deduced directly from the kinetic energy metric. For systems with nonholonomic constraints an extension to the known nonholonomic momentum equation that includes general forcing functions is given. The classical reduction, where invariants of the dynamics such as momenta of energy are factored out, is extended to include external nonholonomic constraints which are found mainly in robotic systems. So a wide range of applications in the field of mechanics and control of robotic and biological locomotion can be given, such as reorienting satellites with robotic arms, wheeled mobile robots and the snakeboard motions. The latter one is deeply investigated in an example discussion. In contrast to the prior work on this subject the author develops straightforward and efficient methods to generate the equations of motion in a structured or automated way. An overview of the Lagrangian formulation of nonholonomic reduction and matrix equations for the dynamics of systems with symmetries, external forces and constraints are provided. Extra attention is paid to the examination of Rayleigh dissipation functions to model viscous friction in locomotion systems.
scientific article; zbMATH DE number 1293240
scientific article