  We investigate the dynamics of finite degree-of-freedom, planar mechanical
systems with multiple sliding, unilateral frictional point contacts. A complete
classification of systems with 2 sliding contacts is given. The contact-mode
based approach of rigid body mechanics is combined with linear stability
analysis using a compliant contact model to determine the feasibility and the
stability of every possible contact mode in each class. Special forms of
non-stationary contact dynamics including "impact without collision" and
"reverse chattering" are also investigated. Many types of solution
inconsistency and the indeterminacy are identified and new phenomena related to
Painlev\'e"s non-existence and non-uniqueness paradoxes are discovered. Among
others, we show that the non-existence paradox is not fully resolvable by
considering impulsive contact forces. These results contribute to a growing
body of evidence that rigid body mechanics cannot be developed into a complete
and self-consistent theory in the presence of contacts and friction.
