%0 Journal Article
%T Symmetric Reduction and Hamilton-Jacobi Equation of Underwater Vehicle with Internal Rotors
%A Hong Wang
%J Mathematics
%D 2013
%I arXiv
%X In this paper, we first give the regular point reduction by stages and Hamilton-Jacobi theorem of regular controlled Hamiltonian (RCH) system with symmetry on the generalization of a semidirect product Lie group. Next, as an application of the theoretical result, we consider the underwater vehicle with two internal rotors as a regular point reducible by stages RCH system, by using semidirect product Lie group and Hamiltonian reduction by stages. In the cases of coincident and non-coincident centers of buoyancy and gravity, we give explicitly the motion equation and Hamilton-Jacobi equation of reduced underwater vehicle-rotors system on a symplectic leaf by calculation in detail, respectively, which show the effect on controls in regular symplectic reduction by stages and Hamilton-Jacobi theory.
%U http://arxiv.org/abs/1310.3014v3