ON A GENERALIZATION OF BERTRAND’S THEOREM

ON A GENERALIZATION OF BERTRAND'S THEOREM

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摘要 Bertrand's theorem for the determination of the applied forces to a holonomic system from one of its first integrals, is extended to nonholonomic systems. Some interesting applications of this new result are also given. Bertrand's theorem for the determination of the applied forces to a holonomic system from one of its first integrals, is extended to nonholonomic systems. Some interesting applications of this new result are also given.

作者史荣昌梅凤翔

机构地区 Peking Institute of Technology

出处《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1993年第6期537-544,共8页 应用数学和力学（英文版）

基金 National Natural Science Foundation of China

关键词 analytical mechanics nonholonomic system first integral inverse problem of dynamics analytical mechanics, nonholonomic system, first integral, inverse problem of dynamics

分类号 O3，O1 [理学—力学]

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1M.VESKOVI,V.OVI,A.OBRADOVI.Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces[J].Applied Mathematics and Mechanics(English Edition),2011,32(2):211-222.
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3XIA Li-Li WANG Xian-Jun ZHAO Xian-Lin.Symmetries and Mei Conserved Quantities for Nonholonomic Systems with Servoconstraints[J].Communications in Theoretical Physics,2009,51(1):1-5.
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5梅凤翔.ONE TYPE OF INTEGRALS FOR THE EQUATIONS OF MOTION OF HIGHER-ORDER NONHOLONOMIC SYSTEMS[J].Applied Mathematics and Mechanics(English Edition),1991,12(8):799-806.
6庞婷,张明江,蔺鹏,路凯.Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates[J].Chinese Physics Letters,2009,26(7):9-12.
7刘畅,常鹏,刘世兴,郭永新.Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems[J].Chinese Physics B,2010,19(3):21-26.
8PANG Ting FANG Jian-Hui ZHANG Ming-Jiang LIN Peng LU Kai.Perturbation to Mei Symmetry and Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates[J].Communications in Theoretical Physics,2009,52(11):779-783.
9朱海平.SZEBEHELY'S PROBLEM FOR NONHOLONOMICSYSTEMS WITH A GIVEN FIRST INTEGRAL[J].Applied Mathematics and Mechanics(English Edition),1998,19(9):843-849.
10张毅.Stability of Manifold of Equilibrium States for Nonholonomic Systems in Relative Motion[J].Chinese Physics Letters,2009,26(12):27-30. 被引量：1

Applied Mathematics and Mechanics(English Edition)

1993年第6期

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