Stability of motion for a constrained Birkhoff's system in terms of independent variables
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This paper proposes firstly the Pfaff-Birkhoff-D'Alembert's principle and obtains the equations of motion in terms of the independent variables for a constrained Birkhoff's system from the principle. Secondly, it establishes the equations of perturbation of the system. Finally, it obtains the stability criteria by using the Liapunov direct method and the firstly approximate method.
Key wordsdynamics Birkhoff's system stability of motion
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- G. D. Birkhoff,Dynamical Systems, AMS College Publ., Providence RI (1927), 89–91.Google Scholar
- R. M. Santilli,Foundation of Theoretical Mechanics II, Springer-Verlag New York (1983), 30–40.Google Scholar
- A. S. Galiullin,Analytical Dynamics, Vyshaya Shkola, Moscow (1989), 249–263. (in Russian)Google Scholar
- Mei Fengxiang and Shi Rongchang. On the Pfaff-Birkhoff principle.J. of BIT,13 (211) (1993), 256–273. (in Chinese)Google Scholar
- Dai Xianyang, Zhao Guankang and Mei Fengxiang, Birkhoff representation for Chaplygin's nonholonomic systems,Thirty Years for Nonholonomic Mechanics in China, Henan Univ. Press, Kaifeng (1994), 107–109, (in Chinese)Google Scholar
- Mei Fengxiang, Inverse problem of dynamics for Birkhoff's systems,J. of Peking Teachers College,13, 4 (1992), 32–36. (in Chinese)Google Scholar
- Mei Fengxiang, Stability of equilibrium for the autonomous Birkhoff system,Chinese Science Bulletin,38, 10 (1993), 816–819Google Scholar
- Wu Huibin and Mei Fengxiang. Transformation theory of generalized Birkhoffian system.Chinese Science Bulletin,40, 16 (1995), 885–888.Google Scholar