Original manuscript: 2015/06/15
The stability of an equilibrium point of a nonlinear system is typically analyzed in two ways: (1) stability of its linearization, and (2) Lyapunov stability. An unconstrained simple mechanical system is a type of nonlinear system with a special structure, and so the methods for stability analysis can be specialized for this particular class of nonlinear systems. For a simple mechanical system subject to velocity constraints, the situation becomes more complicated. If the constraints are holonomic, then the problem can simply be reduced to that of an unconstrained simple mechanical system by restricting analysis to a certain submanifold of the configuration space. If the constraints are nonholonomic, this approach cannot be taken. In this report we study the differences and additional complexities that arise in these nonholonomic mechanical systems, and derive results with regards to linearization and stability of its equilibria.
Last Updated: Fri Oct 27 09:10:27 2017