Results obtained previously [1,2], which are applicable to mechanical systems containing non-conservative positional forces, are developed and generalized. The necessary and sufficient conditions are formulated for the transition to a certain matrix equation, the use of which enables one to overcome
The stabilization of the equilibrium of conservative systems using gyroscopic forces
β Scribed by S.P. Sosnitskii
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 537 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0021-8928
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β¦ Synopsis
Criteria for the instability of the equilibrium of gyroscopically coupled systems, when the gyroscopic forces may be predominant, are presented. It is sho~a~ that the clear predominance of gyroscopic forces over potential forces still does not ensure stability of the equilibrium. The structure of the potential forces remains the key here. As an example, the problem of the stability of the steady-state motions of an artificial satellite is considered.
π SIMILAR VOLUMES
In this paper, we consider the conservative system x q a t x 2nq1 q e t, x s 0, n G 1, ## Ε½ . Ε½ . Ε½ . Ε½ . where a t is a continuous and 1-periodic function in the time t. e t, x is also 1-periodic in the time t and dominated by the power x 2 nq2 in a neighborhood of x s 0. A sufficient and neces
The exponential stability of the unperturbed motion of a non-autonomous mechanical system with a complete set of forces, that is, dissipative, gyroscopic, potential and non-conservative positional forces, is investigated. The problem of stabilizing a nonautonomous system with specified non-conservat