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A Functional Interpolation Approach to Compute Periodic Orbits in the Circular-Restricted Three-Body Problem

Author

Listed:
  • Hunter Johnston

    (Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA)

  • Martin W. Lo

    (Mission Design and Navigation Section, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91125, USA)

  • Daniele Mortari

    (Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA)

Abstract

In this paper, we develop a method to solve for periodic orbits, i.e., Lyapunov and Halo orbits, using a functional interpolation scheme called the Theory of Functional Connections (TFC). Using this technique, a periodic constraint is analytically embedded into the TFC constrained expression. By doing this, the system of differential equations governing the three-body problem is transformed into an unconstrained optimization problem where simple numerical schemes can be used to find a solution, e.g., nonlinear least-squares is used. This allows for a simpler numerical implementation with comparable accuracy and speed to the traditional differential corrector method.

Suggested Citation

  • Hunter Johnston & Martin W. Lo & Daniele Mortari, 2021. "A Functional Interpolation Approach to Compute Periodic Orbits in the Circular-Restricted Three-Body Problem," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1210-:d:563227
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    Cited by:

    1. Daniele Mortari, 2022. "Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives," Mathematics, MDPI, vol. 10(24), pages 1-16, December.

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