Averaging Method in the Problem of the Lorentz Stabilization of the Indirect Equilibrium Position of a Satellite in the Orbital Coordinate System

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Abstract

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.

Original languageEnglish
Pages (from-to)95-105
Number of pages11
JournalVestnik St. Petersburg University: Mathematics
Volume54
Issue number1
DOIs
StatePublished - Jan 2021

Scopus subject areas

  • Mathematics(all)

Keywords

  • asymptotic stability
  • Lyapunov function method
  • rotary motion
  • satellite
  • stabilization

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