Pseudo-arclength method convergence for continuous, piecewise-differentiable systems

Continuation algorithms such as the pseudo-arclength method are frequently used to analyze nonlinear dynamical systems and to solve optimal control problems. They require continuous differentiability of the equations to be solved and may stall if this assumption is violated. This paper analyzes the conditions under which the pseudo-arclength method succeeds or fails when applied to a system of equations that is continuous but only piecewise differentiable. A strategy to alleviate this problem is derived based on the insights gained.