Method of Variation of Constants

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A technique that replaces constant parameters in differential equations with undetermined functions. In this paper, the amplitudes and phases of the first-order approximate periodic orbit solution near libration points are treated as time-varying functions, fitted by polynomials to capture the spiral nature of transfer trajectories, thereby constructing shape functions applicable to Gauss pseudospectral method.

Application Value

The method of variation of constants serves as an important bridge connecting analytical approximation and numerical computation. In transfer trajectory design for periodic orbits near libration points, linearized periodic orbit solutions have fixed amplitudes and phases, while actual transfer trajectories often gradually diverge from or converge to periodic orbits along spirals. By treating constants as time-varying functions and fitting their variation patterns with polynomials, shape functions conforming to actual dynamics can be constructed for use with numerical optimization methods such as Gauss pseudospectral method. This method effectively reduces the difficulty of solving periodic orbit transfer problems and holds important application value in halo orbit deployment and L1/L2 halo orbit insertion missions.

  • Gauss Pseudospectral Method
  • Periodic Orbit
  • Halo Orbit
  • Shape Function

References

  • Gauss Pseudospectral Method for Low-Thrust Transfer Between Periodic Orbits Near Libration Points
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Contributors: ouyangjiahong, Ou Yang Jiahong