Symmetric Reduction and Hamilton-Jacobi Equations of the Controlled Underwater Vehicle-Rotor System  

作　　者：Hong Wang 

机构地区：[1]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China.

出　　处：《Communications in Mathematical Research》2023年第4期575-644,共70页数学研究通讯（英文版）

摘　　要：.As an application of the theoretical results,in this paper,we study the symmetric reduction and Hamilton-Jacobi theory for the underwater ve-hicle with two internal rotors as a regular point reducible RCH system,in the cases of coincident and non-coincident centers of the buoyancy and the gravity.At first,we give the regular point reduction and the two types of Hamilton-Jacobi equations for a regular controlled Hamiltonian(RCH)system with sym-metry and a momentum map on the generalization of a semidirect product Lie group.Next,we derive precisely the geometric constraint conditions of the reduced symplectic forms for the dynamical vector fields of the regular point reducible controlled underwater vehicle-rotor system,that is,the two types of Hamilton-Jacobi equations for the reduced controlled underwater vehicle-rotor system,by calculations in detail.These work reveal the deeply internal relationships of the geometrical structures of the phase spaces,the dynamical vector fields and the controls of the system.

关 键 词：Underwater vehicle with internal rotors regular controlled Hamiltonian system coincident and non-coincident centers regular point reduction Hamilton-Jacobi equation 

分 类 号：O175.26[理学—数学] O231[理学—基础数学]