  The theory of feedback integrators is extended to handle mechanical systems
with nonholonomic constraints with or without symmetry, so as to produce
numerical integrators that preserve the nonholonomic constraints as well as
other conserved quantities. To extend the feedback integrators, we develop a
suitable extension theory for nonholonomic systems, and also a corresponding
reduction theory for systems with symmetry. It is then applied to various
nonholonomic systems such as the Suslov problem on SO(3), the knife edge, the
Chaplygin sleigh, the vertical rolling disk, the roller racer, the Heisenberg
system, and the nonholonomic oscillator.
