Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conserva...Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three cases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints.展开更多
The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative,conservative,and circulatory forces.The method is based on the existence of solutions to the di...The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative,conservative,and circulatory forces.The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity.It is assumed that the kinetic energy,the Rayleigh dissipation function,and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions.The results obtained here are partially generalized the results obtained by Kozlov et al.(Kozlov,V.V.The asymptotic motions of systems with dissi-pation.Journal of Applied Mathematics and Mechanics,58(5),787-792(1994).Merkin,D.R.Introduction to the Theory of the Stability of Motion(in Russian),Nauka,Moscow(1987).Thomson,W.and Tait,P.Treatise on Natural Philosophy,Part I,Cambridge University Press,Cambridge(1879)).The results are illustrated by an example.展开更多
基金Project supported by the Ministry of Science and Technological Development of the Republic of Serbia (Nos. 144019, 20152, and 114052)
文摘Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three cases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints.
基金supported by the Ministry of Science and Technological Development of the Republic of Serbia (Nos.ON174016 and TR35006)
文摘The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative,conservative,and circulatory forces.The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity.It is assumed that the kinetic energy,the Rayleigh dissipation function,and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions.The results obtained here are partially generalized the results obtained by Kozlov et al.(Kozlov,V.V.The asymptotic motions of systems with dissi-pation.Journal of Applied Mathematics and Mechanics,58(5),787-792(1994).Merkin,D.R.Introduction to the Theory of the Stability of Motion(in Russian),Nauka,Moscow(1987).Thomson,W.and Tait,P.Treatise on Natural Philosophy,Part I,Cambridge University Press,Cambridge(1879)).The results are illustrated by an example.
