Dynamical Equations of Controlled Rigid Spacecraft with a Rotor

TL;DR

This paper develops a geometric framework for analyzing controlled rigid spacecraft with internal rotors, deriving reduction and Hamilton-Jacobi equations to understand the system's dynamics in different buoyancy and gravity configurations.

Contribution

It introduces a regular point reduction approach and derives Hamilton-Jacobi equations for controlled spacecraft-rotor systems, revealing deep geometric relationships.

Findings

Derived dynamical vector fields for reduced systems

Established geometric constraint conditions for symplectic forms

Formulated Hamilton-Jacobi equations for control analysis

Abstract

In this paper, we consider the controlled rigid spacecraft with an internal rotor as a regular point reducible regular controlled Hamiltonian (RCH) system. In the cases of coincident and non-coincident centers of buoyancy and gravity, we first give the regular point reduction and the dynamical vector field of the reduced controlled rigid spacecraft-rotor system, respectively. Then, we derive precisely the geometric constraint conditions of the reduced symplectic form for the dynamical vector field of the regular point reducible controlled spacecraft-rotor system, that is, the two types of Hamilton-Jacobi equation for the reduced controlled spacecraft-rotor system by calculation in detail. These researches reveal the deeply internal relationships of the geometrical structures of phase spaces, the dynamical vector fields and controls of the system.