Abstract
This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem. We show remarkable connections between these two problems manifested by the associated Hamiltonians obtained by the Maximum Principle of optimal control. We also show that each of these Hamiltonians is completely intergrable, in the sense of Liouville. Finally we demonstrate the significance of these results for the theory of mechanical systems.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference32 articles.
1. The geometry of the Ball-Plate Problem;Jurdjevic;Arch. Ration. Mech. Anal.,1993
2. Non-Euclidean Elasticae;Jurdjevic;Am. J. Math.,1995
3. Jurdjevic, V. (1997). Geometric Control Theory, Cambridge University Press. Cambridge Studies in Advanced Mathematics.
4. Integrable Hamiltonian Systems on Lie groups: Kowalewski type;Jurdjevic;Ann. Math.,1999
5. Optimal control of the sphere Sn rolling on En;Zimmerman;Math. Control Signals Syst.,2005
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献