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Averaging Method in the Problem of the Lorentz Stabilization of the Indirect Equilibrium Position of a Satellite in the Orbital Coordinate System
Vestnik St. Petersburg University, Mathematics Pub Date : 2021-03-16 , DOI: 10.1134/s1063454121010027
A. Yu. Aleksandrov , N. R. Andriyanova , A. A. Tikhonov

Abstract

A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem of the Lorentzian stabilization of the satellite in the orbital coordinate system in the indirect equilibrium position is solved under the conditions of the perturbing effect of the gravitational torque. To solve this problem, which is characterized by incomplete control, a method of averaging differential equations is developed. Using the original construction of the unsteady Lyapunov function, we obtain sufficient conditions for the asymptotic stability of the programmed satellite motion mode in the form of constructive inequalities with respect to the control parameters.



中文翻译:

轨道坐标系中卫星间接平衡位置的洛仑兹稳定问题的平均方法

摘要

考虑在小倾角的圆形轨道上的动态对称卫星。在引力转矩的扰动作用条件下,解决了卫星在间接平衡位置在轨道坐标系中的洛伦兹稳定问题。为了解决以控制不完全为特征的问题,提出了一种平均微分方程的方法。使用非定常Lyapunov函数的原始构造,我们以相对于控制参数的构造性不等式的形式,获得了已编程卫星运动模式渐近稳定性的充分条件。

更新日期:2021-03-16
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