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2002 Volume 11 Issue 12
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Xu Zhi-Xin(许志新), Guo Yong-Xin(郭永新), Wu Wei(吴炜). 2002: A connection theory for a nonlinear differential constrained system, Chinese Physics B, 11(12): 1228-1233.
Citation: Xu Zhi-Xin(许志新), Guo Yong-Xin(郭永新), Wu Wei(吴炜). 2002: A connection theory for a nonlinear differential constrained system, Chinese Physics B, 11(12): 1228-1233.
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A connection theory for a nonlinear differential constrained system

  • Department No. 1, East China Shipbuilding Institute, Zhenjiang 212003, China

  • Department of Physics, Liaoning University, Shenyang 110036, China

  • Available Online: 30/12/2002
  • Fund Project: the National Natural Science Foundation of China(Grant 10175032)%the Natural Science Foundation of Liaoning Province, China(Grant 002083 and 2001101024)%the Science Research Foundation of Liaoning Education Bureau, Chin
  • 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-δ 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.
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A connection theory for a nonlinear differential constrained system

  • Available Online: 30/12/2002

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-δ 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.

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