讲座题目：A Practical Example: Controlled Rigid Spacecraft-Rotor System

主讲人：王红

讲座时间：9月25日周六下午15：00—16：00

讲座地点：腾讯会议 ID：710 843 457

主讲人简介：

    王红：1992年毕业于复旦大学数学研究所获理学博士学位，从师于胡和生院士。研究方向：微分几何。毕业后一直从事数学专业的本科、研究生的教学和科研工作。1997年12月晋升为教授，1999年12月遴选为博士生导师。2001年7月至今，在南开大学数学科学学院工作，任教授、应用数学专业博士生导师。近年来一直从事用微分几何方法研究非线性动力控制系统和力学系统的几何理论研究工作，获得一系列研究成果。曾应邀访问意大利、荷兰、加拿大、西班牙等多个数学研究所，进行合作研究和学术交流。

主讲内容：

    A controlled Hamiltonian (CH) system is a Hamiltonian system with external force and control. In general, a CH system under the actions of external force and control is not Hamiltonian, however, it is a dynamical system closely related to a Hamiltonian system, and it can be explored and studied by extending the methods for external force and control in the study of Hamiltonian systems. Thus, we can emphasize explicitly the impact of external force and control in the study of CH systems. As an application of the theoretical results for regular Hamiltonian reduction and Hamilton- Jacobi theory of the CH system, in this report, we consider the controlled rigid spacecraft with an internal rotor as a regular point reducible regular controlled Hamiltonian (RCH) system. 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 equations. These researches reveal the deeply internal relationships of the geometrical structures of phase spaces, the dynamical vector fields and controls of the system.