整体微分几何 meaning in English
global differential geometry
Examples
- R [ 16 ] we deprive the mathematical model of altitude and shape control of satellite with articulated appendages although not essential , the model formulation using li group and li algebra theory leads to relatively simple and available control formulas
R ，利用整体微分几何的相关理论推导了带有关节相连的附属物的人造卫星姿态?形状控制系统的数学模型，该模型的优点是易于采用简单有效的控制方法。 - Secondly , we introduce the theory that flat systems , an important subclass of nonlinear systems introduced via differential algebraic methods , are defined in a infinite dimensional differential geometrical framework . utilizing this method , the control system of the vtol aircraft becomes a linear control system . finally , we introduce the theory that is found by my teacher , wanghong professor
3 、应用平坦性分析方法和整体微分几何方法分别分析了pvtol飞机在其起飞过程时的控制律，得到了该系统的整体化方程，指出了该系统是能控能观的，并且指出该系统是平坦的控制系统，可以通过动态状态反馈和适当的坐标变换使之变成线性系统。 - This thesis deals with the following results with regard to the control systems of satellite : ( 1 ) on the basis of global geometry theory , deprive the representation of state equation for the satellite orbit control system under the geometric restraint , show that the geometrical structure of geometric restraint affect on satellite orbit control system , and study the connection between the equilibriums state of the control system and the geodesies of the geometric restraint
对于人造卫星控制系统的研究，本论文的主要工作表现在以下几个方面： ( 1 )基于整体微分几何理论推导出人造卫星轨道控制系统在几何约束下的整体化方程，展示了几何约束条件对人造卫星轨道控制系统的影响。并且讨论了具有几何约束的人造卫星轨道控制系统的平衡态与几何约束条件之间的关系。 - In the part of orbit control , the main ideas in study is to define the nonlinear control system on a riemann manifold from the global viewpoint , and to build the intimate relation between the geometrical structure of state space and the state equation of nonlinear control system ; in the part of attitude control , the main ideas in study is to deduce mathematical model with good character based on global differential geometry ideas as well as li group and li algebra , moreover , to design corresponding control schemes
在轨道控制部分，研究的主要思想是从整体化的观点出发定义一种建立在riemann流形上的非线性控制系统，将状态空间的几何结构与控制系统的状态方程建立直接的联系。在姿态控制部分，研究的主要思想是以整体微分几何方法为工具，以李群与李代数等数学理论为基础，从数学角度建立具有良好性能的数学模型，并设计出相应的控制方法。