riemann manifold meaning in English

黎曼流形

9 . by the research of metric tensor and riemann tensor on riemann manifold , we get the inherent curvature of configuration space belonging to parallel mechanism . so the relative coordinates and generalized coordinates are inevitable choice for parallel mechanism . 10
9 、通过对度量张量和riemann张量的研究，得出并联机构运动可达子空间的内在“弯曲”性质，指出使用相对坐标系和广义坐标是研究并联机构运动学和动力学问题的必然选择。
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。