On instability of conservative systems with gyroscopic forces
Theorems on equilibrium instability of conservative systems with gyroscopic forces are proved. The theorems obtained are nonlinear analogs of the Kelvin theorem. The equilibrium instability of the Chaplygin nonholonomic systems is considered.
KeywordsConstraint Equation Function Versus Conservative System Nonholonomic System Constraint Factor
Unable to display preview. Download preview PDF.
- 1.L. A. Pars, A Treatise on Analytical Dynamics, Heinemann, London (1964).Google Scholar
- 3.N. G. Chetaev, Stability of Motion. Works on Analytic Mechanics [in Russian], Academy of Sciences of the USSR, Moscow (1962).Google Scholar
- 4.S. P. Sosnyts'kyi, «On gyroscopic stabilization of conservative systems,” Ukr. Mat. Zh., 48, No. 10, 1402–1408 (1996).Google Scholar
- 5.V. I. Arnol'd, Mathematical Methods in Classical Mechanics [in Russian], Nauka, Moscow (1974).Google Scholar
- 7.N. N. Krasovskii, Some Problems of the Theory of Stability of Motion [in Russian], Fizmatgiz, Moscow (1959).Google Scholar
- 11.S. P. Sosnitskii, “On unstable equilibrium of natural systems,” in: Problems of the Investigation of Stability and Stabilization of Motion [in Russian], Computing Center of Academy of Sciences of the USSR, Moscow (1991), pp. 48–61.Google Scholar
- 12.N. A. Kil'chevskii, Course of Theoretical Mechanics [in Russian], Nauka, Moscow (1977).Google Scholar
- 13.Yu. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems [in Russian], Nauka, Moscow (1967).Google Scholar
- 14.A. V. Karapetyan, “Some problems of the stability of motion of nonholonomic systems,” in: Theory of Stability and Its Applications [in Russian], Novosibirsk (1979), pp. 184–190.Google Scholar