Basic concepts about the creep behavior of nonholonomic constrained (NC) systems were discussed previously by us (1995). Two fundamental types of creep kinematics were proposed and the hybrid one could be developed. In this work, we extend to the creep dynamics of typical NC systems such as the disk, sleigh and wheel. First, certain reduced models of constrained motion such as ideal, relative, pair, and general-pair models are explored and related. Secondly, by the invariant manifold method of singular perturbation, fundamental rotational and traverse creep dynamics and a hybrid one are calculated in an approximate way. They can be close to the complete system as possible. Therefore, the bridge between reduced and invariant analyses can be made by the model of general-pair creep and can help us understand physical implications behind the approximate solutions. It is proven that advanced vehicle techniques, such as the anti-lock braking system and a special tracking control system, can be realized by the proposed quasi-constrained creeps.
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