We study the problem of optimal control of a Chaplygin ball on a plane by means of 3 internal rotors. Using Pontryagin maximum principle, the equations of extremals are reduced to Hamiltonian equations in group variables. For a spherically symmetric ball, the solutions can be expressed in by elliptic functions.
Keywords:
nonholonomic constraint, vaconomic mechanics, optimal control, maximum principle, Hamiltonian
Citation:
Bolotin S. V., The problem of optimal control of a Chaplygin ball by internal rotors, Rus. J. Nonlin. Dyn.,
2012, Vol. 8, No. 4,
pp. 837-852
DOI:10.20537/nd1204011