THE DIFFERENTIAL GEOMETRIC PRINCIPLE OF THE NONHOLONOMIC MECHANICAL SYSTEMS OF CHETAEV’S TYPE

摘要/Abstract

摘要： This paper deals with the nonholonomic mechanical systems of Chetaev’s type by use of modern differential geometric methods. Based on a precise definition of Chetaev-type constraint pfaffian systems, the differential geometric structure is given for the description of nonholonomic mechanical systems. In thisframwork, the classical theory of Lagrange’s equations with nonholonomic constraints is put into an invariant and coordinate free form. Furthermore, the problems of constraint imbedding and conservation laws are discussed within thisframwork, and the Noether-type thereom on constraint-imbedding submanifolds is obtained.

关键词: BEM, lower bound limit analysis, self-equilibrium stress field, nonlinear programming, complex method

Abstract: This paper deals with the nonholonomic mechanical systems of Chetaev’s type by use of modern differential geometric methods. Based on a precise definition of Chetaev-type constraint pfaffian systems, the differential geometric structure is given for the description of nonholonomic mechanical systems. In thisframwork, the classical theory of Lagrange’s equations with nonholonomic constraints is put into an invariant and coordinate free form. Furthermore, the problems of constraint imbedding and conservation laws are discussed within thisframwork, and the Noether-type thereom on constraint-imbedding submanifolds is obtained.

Key words: BEM, lower bound limit analysis, self-equilibrium stress field, nonlinear programming, complex method

赵世鹰. THE DIFFERENTIAL GEOMETRIC PRINCIPLE OF THE NONHOLONOMIC MECHANICAL SYSTEMS OF CHETAEV’S TYPE[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(9): 903-918.

Zhao Shi-ying . THE DIFFERENTIAL GEOMETRIC PRINCIPLE OF THE NONHOLONOMIC MECHANICAL SYSTEMS OF CHETAEV’S TYPE[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(9): 903-918.

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