ISSN:
1573-8698
Keywords:
nonconservative mechanical systems
;
stability
;
Lyapunov functions
;
attraction domain
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract Mechanical systems subjected to dissipative, gyroscopic, conservative, and also nonconservative positional forces are considered. The question of the effect of dissipative, gyroscopic, and conservative forces on the motion stability of a mechanical systems is determined by classical Kelvin–Chetaev theorems [1]. The presence of nonconservative positional forces considerably complicates the situation and excludes direct application of these theorems. Applying Lyapunov's functions method the condition of asymptotic stability of a mechanical system under the action of all listed above forces is obtained. Moreover, the estimation of the attraction domain in phase space is found. The precession system which is used in the solution of some problems in the applied theory of the gyroscopic systems is also examined. The connection between the stability of origin and precession systems is detected. Theoretical results are applied to the stabilization problem of stationary motion of the balanced gimbal suspension gyro by means of external moments.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009500527061
