5 李导数与李代数 正如前面讲过的,定义在微分流形上的动态系统完全可以由定义在该流形上的向量场描述。给定一个向量场就代表了给定一个动态系统。实际上,向量场的局部坐标表示就是一阶微分方程组的等式右侧,若右侧含有控制量,那就是一个控制系统,当控制量改变时,方程右侧也 5 Derivatives and Lie Algebra As we said before, the dynamical systems defined on differential manifolds can be completely described by vector fields defined on the manifold. Given a vector field represents a given dynamic system. In fact, the local coordinate of the vector field is the right side of the equation of first order differential equations. If the right side contains the control amount, then it is a control system. When the control amount changes, the right side of the equation