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Meyer, K.R. and Schmidt, D.S. (1986) The Stability of the Lagrange Triangular Point and a Theorem of Arnold. Journal of Differential Equations, 62, 222-236.
https://doi.org/10.1016/0022-0396(86)90098-7

has been cited by the following article:

• TITLE: Port-Hamiltonian Based Control of the Sun-Earth 3D Circular Restricted Three-Body Problem: Stabilization of the L1 Lagrange Point

  AUTHORS: Haotian Yan

  KEYWORDS: Port-Hamiltonian, Lagrange Points, Circular Restricted Three-Body Problem (CRTBP), Linear Quadratic Regulator (LQR)

  JOURNAL NAME: Modern Mechanical Engineering, Vol.10 No.3, August 31, 2020

  ABSTRACT: In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through energy-shaping and dissipation injection. The closed-loop Hamiltonian is a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that the Port-Hamiltonian approach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback system based on Port-Hamiltonian approach is also robust against white noise in the inputs.