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

Hunter Johnston, Martin W. Lo and Daniele Mortari
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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

Mathematics, 2021, vol. 9, issue 11, 1-17

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.

Keywords: functional interpolation; Theory of Functional Connections; ordinary differential equations; least-squares (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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