  This paper extends continuous contraction theory of nonlinear dynamical
systems to systems with nonlinear inequality constraints. It shows that the
contraction behaviour of the constrained dynamics is given by the covariant
derivative of the system dynamics from the original contraction theorem [4],
plus the second covariant derivative of the active inequality constraint.
Practical applications include controllers constrained to an operational
envelope, trajectory control with moving obstacles, and a classical Lagrangian
interpretation of the single and two slit experiments of quantum mechanics.
