Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Whittaker, E. T.,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Fourth edition, Cambridge Press (1952).
Galiullin, A. S.,Methods of Solution of Inverse Problems of Dynamics, M. Nauka (1986). (in Russian)
Yerugin, N. P., Constitution of all set of systems of differential equations having a given integral curve,P. M. M. 16, 6 (1952), 659–670. (in Russian)
Mei Feng-xiang,Foundations of Mechanics of Nonholonomic Systems, Peking Institute of Technology Press (1985). (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Fan Da-jun
Project supported by the National Natural Science Foundation of China.
Rights and permissions
About this article
Cite this article
Rong-chang, S., Feng-xiang, M. On a generalization of Bertrand's theorem. Appl Math Mech 14, 537–544 (1993). https://doi.org/10.1007/BF02451362
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02451362