Uniaxial Attitude Stabilization of a Rigid Body under Conditions of Nonstationary Perturbations with Zero Mean Values
- 1 Downloads
This paper deals with the problem of uniaxial stabilization of the angular position of a rigid body exposed to a nonstationary perturbing torque. The perturbing torque is represented as a linear combination of homogeneous functions with variable coefficients. It is assumed that the order of homogeneity of perturbations does not exceed the order of homogeneity of the restoring torque, and the variable coefficients in the components of the disturbing torque have zero mean values. A theorem on sufficient conditions for the asymptotic stability of a programmed motion of the body is proven using the Lyapunov direct method. The determined conditions guaranteeing the solution to the problem of body uniaxial stabilization do not impose any restrictions on the amplitudes of oscillations of the disturbance torque coefficients. Results of numerical modeling are presented that confirm the conclusions obtained analytically.
Keywordsuniaxial stabilization attitude motion nonlinear perturbations asymptotic stability
Unable to display preview. Download preview PDF.
- 5.L. D. Akulenko, D. D. Leshchenko, and F. L. Chernous’ko, “Perturbed motions of a rigid body that a close to regular precession,” Mech. Solids 21 (5), 1–8 (1986).Google Scholar
- 6.A. A. Tikhonov, “Resonance phenomena in oscillations of a gravity-oriented rigid body. Part 4: Multifrequency resonances,” Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron., No. 1, 131–137 (2000).Google Scholar
- 8.A. A. Tikhonov, “On the rotary motion of a shielded artificial earth satellite in a noncentral gravitational field,” Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron., No. 3, 81–87 (2004).Google Scholar
- 12.M. M. Khapaev, Asymptotic Methods and Stability in Theory of Nonlinear Oscillations (Vysshaya Shkola, Moscow, 1988) [in Russian].Google Scholar
- 16.A. Yu. Aleksandrov, “On the asymptotical stability of solutions of nonstationary differential equation systems with homogeneous right hand sides,” Dokl. Ross. Akad. Nauk 349, 295–296 (1996).Google Scholar
- 25.E. Ya. Smirnov, Some Problems of the Mathematical Control Theory (Leningr. Gos. Univ., Leningrad, 1981) [in Russian].Google Scholar
- 26.V. I. Zubov, Stability of Motion (Vysshaya Shkola, Moscow, 1973) [in Russian].Google Scholar