Abstract 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.
Received: 14 May 2002
Revised: 16 August 2002
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10175032), the Natural Science Foundation of Liaoning Province, China (Grant Nos 002083 and 2001101024), and the Science Research Foundation of Liaoning Education Bureau, China (Grant Nos 990111004 and 20021004).
Cite this article:
Xu Zhi-Xin (许志新), Guo Yong-Xin (郭永新), Wu Wei (吴炜) A connection theory for a nonlinear differential constrained system 2002 Chinese Physics 11 1228
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