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


  • 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.

published proceedings


author list (cited authors)

  • Johnston, H., Lo, M. W., & Mortari, D.

citation count

  • 1

complete list of authors

  • Johnston, Hunter||Lo, Martin W||Mortari, Daniele

publication date

  • January 2021