Strobe Map

Author: CislunarSpace

Website: https://cislunarspace.cn

Definition

The strobe map is a time-fixed map used to simplify the computation of quasi-periodic orbits, such as Lissajous orbits near libration points. By sampling the state at fixed time intervals equal to the orbital period T, the strobe map φ_T maps an initial state to its state after one period. The problem of finding quasi-periodic orbits then reduces to finding invariant curves under this discrete map. Combined with Fourier series representation and Newton-like iteration, the strobe map enables efficient numerical computation and continuation of quasi-periodic orbit families.

Key Properties

  • Samples the flow at fixed time intervals, converting continuous dynamics to a discrete map.
  • Periodic orbits correspond to fixed points of the map; quasi-periodic orbits correspond to invariant curves.
  • Fourier series representation of invariant curves enables systematic numerical computation.
  • Facilitates continuation of orbit families by tracking invariant curves as parameters vary.

References

  • Gómez, G., Mondelo, J. M., and Simó, C. "A Collocation Method for the Numerical Computation of Orbits in the Restricted Three Body Problem." Physica D, 157:283–322, 2001.