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

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.

authors

• Mortari, Daniele

published proceedings

• MATHEMATICS

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

publisher

• MDPI  Publisher

published in

• MATHEMATICS  Journal

keywords

• Functional Interpolation
• Least-squares
• Ordinary Differential Equations
• Theory Of Functional Connections

Digital Object Identifier (DOI)

• 10.3390/math9111210

start page

• 1210

end page

• 1210

volume

• 9

issue

• 11

URL

• http://dx.doi.org/10.3390/math9111210