The Frequency-Amplitude Response of a Class of Nonholonomic Systems

Nonholonomic systems have been investigated as models for locomotion due to the similarity between nonholonomic constraints and the no-slip condition of wheels or the Kutta condition of swimmers' tails. The focus of most past research has been on kinematic nonholonomic systems. However, an increasing body of research points to benefits that dynamic components of these systems, such as underactuated degrees of freedom, can provide.This work investigates the effect of adding stiff degrees of freedom to the Chaplygin sleigh, a classical nonholonomic system that has been used in the past as a swimming model. Observed resonance behavior is shown to greatly increase net velocity of the sleigh at certain ranges of forcing frequency and amplitude.A change to the formulation of the nonholonomic constraint is also considered where the constraint point is defined as fixed with respect to the flow field around the body, which is defined by potential flow theory. The reduced effective inertia resulting from this change improves performance at high forcing frequency, but reduces performance for slower forcing.