Lissajous motion near Lagrangian point $$ L_{2} $$ L 2 in radial solar sail

Abstract

An attempt was made to study the dynamics close to the collinear libration point $$ L_{2} $$ of the radial solar sail circular-restricted three-body problem (RSCRTBP) in the Sun–Jupiter System, where the third massless body is a solar sail. We analyse the qausi-periodic (Lissajous solutions) orbits about the libration point $$ L_{2} $$ . The Lindstedt–Poincare approximation for the qausi-periodic orbits was used for numerical simulations. We utilized linear quadratic regulator (LQR) to stabilize the full nonlinear model, and linear state-feedback controller was designed to stabilize the trajectory.