Harmonic balance analysis and simulations of spacecraft rendezvous and formation flying dynamics

Abstract

In this paper, approximated nonlinear spacecraft relative motion model is developed via Euler Lagrange approach using local vertical–local horizontal frame attached to the chief spacecraft. Harmonic balance analysis approach, a powerful technique for approximating nonlinear equation and generating periodic solutions, is applied to the approximated nonlinear relative motion for the development of new linear harmonic balance approximation model and investigation of its periodic solutions. Using power series method, power series approximate solutions of the harmonically balanced model of the relative motion are developed. Furthermore, the computational algorithm employed for the orbit propagation of nonlinear, harmonic balance and Clohessy–Wilshire models is presented. Using MATLAB ODE45 integrator, the relative motion models are numerically integrated and propagated. The numerical results show that harmonic balance model gave a better approximation of the nonlinear model.

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Correspondence to Ayansola D. Ogundele.

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This is a revised and improved version of the paper AAS 16-436 presented at 26th AAS/AIAA Space Flight Mechanics Meeting held between February 14–18, 2016, Napa, CA.

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Ogundele, A.D. Harmonic balance analysis and simulations of spacecraft rendezvous and formation flying dynamics. AS (2021). https://doi.org/10.1007/s42401-021-00083-0

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Keywords

  • Nonlinear approximation
  • Relative motion
  • Harmonic balance
  • Power series
  • Rendezvous