Dynamical Equations of Controlled Rigid Spacecraft with a Rotor

2020/05/04 by Wang, Hong
#70H20 #70H33 #70Q05 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2005.02221

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.

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