SPHERE, CYLINDROID, CONE AND NONLINEAR CONTROL SYSTEM
球面、柱面、锥面与非线性控制系统

In this paper, from the global viewpoint we first define the nonlinear control system on a two dimensional surface in the three dimensional Euclidean space, give the representation of the state equation under a local coordinate system of the surface, and study the connection between the equilibrium state of the nonlinear system and the geodesics on the surface. Secondly, we show the intimate relation between the nonlinear control system and the special geometrical structure and singular structure of a sphere, a cylindroid and a cone. Moreover, we discuss the local and global controllability and observability of the nonlinear system on the sphere, the cylindroid and the cone.