In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems undergoing contact/impact motion. The method rigorously modeled all motion regimes of hybrid multiple body systems (i.e. free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations. The contact/impact regime was modeled via the idea of instantaneous non-holonomic constraint application. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this paper, the above mentioned method is extended to include the higher order continuum assumptions which eliminates some of the continuum shortfalls from the previous work.

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