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| Based on a serious analysis of the Frobenius integrability condition for affine differential constraints that mechanical systems are subject to, the necessary and sufficient conditions for coincidence of three kinds of unfree variations, the existence of simple symplectic structure of the constraint sub-manifold and equivalence of nonholonomic and vakono- mic dynamics for the constrained systems are respect- iveely obtained, which are all related with partial Frobenius integrability condition in their special forms. Two illustrative examples are presented to verify theresults. |
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| Keywords:affine differential constraints, variations, symplectic structure, nonholonomic and vakonomic dynamics |
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