Within the affine connection framework of Lagrangian control systems, basedon the results of Sussmann on small-time locally controllability of single-input affine nonlinearcontrol systems, the controllability results ...Within the affine connection framework of Lagrangian control systems, basedon the results of Sussmann on small-time locally controllability of single-input affine nonlinearcontrol systems, the controllability results for mechanical control systems with single-input areextended to the case of the systems with isotropic damping, where the Lagrangian is the kineticenergy associated with a Riemannian metric. A sufficient condition of negative small-time locallycontrollability for the system is obtained. Then,it is demonstrated that such systems are small-timelocally configuration controllable if and only if the dimension of the configuration manifold isone. Finally, two examples are given to illustrate the results. Lie bracketting of vector fields andthe symmetric product show the advantages in the discussion.展开更多
文摘Within the affine connection framework of Lagrangian control systems, basedon the results of Sussmann on small-time locally controllability of single-input affine nonlinearcontrol systems, the controllability results for mechanical control systems with single-input areextended to the case of the systems with isotropic damping, where the Lagrangian is the kineticenergy associated with a Riemannian metric. A sufficient condition of negative small-time locallycontrollability for the system is obtained. Then,it is demonstrated that such systems are small-timelocally configuration controllable if and only if the dimension of the configuration manifold isone. Finally, two examples are given to illustrate the results. Lie bracketting of vector fields andthe symmetric product show the advantages in the discussion.
