Analytic approach on geometric structure of invariant manifolds of the collinear Lagrange points

Lü, Jing; Wang, Qi; Wang, Shimin

doi:10.1007/s11433-012-4810-x

Cited by 1 publication

(2 citation statements)

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“…In line with the reasons outlined in the previous subsection, we can neither apply the multiple scales technique nor the Lindstedt-Poincaré method to System (28). Thereby, we will use the place keeping parameters method, after carrying out the relative equations of motion in dimensionless variables.…”

Section: Legitimacy Of Relative Motion Equationsmentioning

confidence: 99%

“…The above equations represent the nonlinear relative motion satellite in dimensionless variables, which are convenient for applying some perturbation techniques, such as multiple scales technique [25][26][27] and KBM methods or Lindstedt-Poincaré [28][29][30][31]. However, we will examine the provided solution by the latter method with the initial conditions of the linear relative motion satellite; these conditions are describe in Equation ( 14).…”

Section: Legitimacy Of Relative Motion Equationsmentioning

confidence: 99%

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Periodic Solutions of Nonlinear Relative Motion Satellites

et al. 2021

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The relative motion of an outline of the rendezvous problem has been studied by assuming that the chief satellite is in circular symmetric orbits. The legitimacy of perturbation techniques and nonlinear relative motion are investigated. The deputy satellite equations of motion with respect to the fixed references at the center of the chief satellite are nonlinear in the general case. We found the periodic solutions of the linear relative motion satellite and for the nonlinear relative motion satellite using the Lindstedt–Poincaré technique. Comparisons among the analytical solutions of linear and nonlinear motions and the obtained solution by the numerical integration of the explicit Euler method for both motions are investigated. We demonstrate that both analytical and numerical solutions of linear motion are symmetric periodic. However, the solutions of nonlinear motion obtained by the Lindstedt–Poincaré technique are periodic and the numerical solutions obtained by integration by using explicit Euler method are non-periodic. Thus, the Lindstedt–Poincaré technique is recommended for designing the periodic solutions. Furthermore, a comparison between linear and nonlinear analytical solutions of relative motion is investigated graphically.

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Section: Legitimacy Of Relative Motion Equationsmentioning

confidence: 99%