Structure-preserving Stabilization of 2-DOF Hyperbolic Hamiltonian System and Its Applications in Solar Sail Three Body Problem

摘要

A structure-preserving controller is constructed to stabilize the hyperbolic Hamiltonian system, and applied to generate bounded orbit in solar sail planar 3 body problem. Based on 2-DOF Hamiltonian system,we obtain:1) the invariant manifolds of the equilibrium can used to stabilize the system just by the position feedback;2) the poles can be assigned at any different positions on the imaginary axis;3)a new type of quasi-periodic orbit is generated, referred as stable Lissajous orbit in this paper, which degenerate to periodic orbit in the cases of resonance(resonant orbit) and suitable initial values ( Lyapunov orbit). The Frobenius norm is used to measure the sensitivity matrix of controller that can also be performed as the optimization index to choose more suitable values for gains. The application of the controller to the solar sail yields that the stable Lissajous orbit is quite different from the classic lissajous orbit, and sail equilibrium in any position can be used to generate bounded orbits. The distributive law of controller is investigated to verify the controller can be implemented in mechanism.