A connection theory for a nonlinear differential constrained system

作者：Xu ZX^*; Guo YX; Wu W

来源：Chinese Physics, 2002, 11(12): 1228-1233.

• nonholonomic constraint
• Ehresmann connection
• integrability condition
• d-delta commutation relation

An Ehresmann connection on a constrained state bundle defined by nonlinear differential constraints is constructed for nonlinear nonholonomic systems. A set of differential constraints is integrable if and only if the curvature of the Ehresmann connection vanishes. Based on a geometric interpretation of d-delta commutation relations in constrained dynamics given in this paper, the complete integrability conditions for the differential constraints are proven to be equivalent to the three requirements upon the conditional variation in mechanics: (1) the variations belong to the constrained manifold; (2) the time derivative commutes with variational operator; (3) the variations satisfy the Chetaev's conditions.

• 出版日期2002-12
• 单位辽宁大学