119899, Moscow, Vorobyevy gory
Lomonosov Moscow State University
Bolotin S. V., Popova T. V.
On the motion of a mechanical system inside a rolling ball
2013, Vol. 9, No. 1, pp. 51-58
We consider a mechanical system inside a rolling ball and show that if the ideal constraints have spherical symmetry, the equations of motion have a Lagrangian form. Without symmetry, this is not true.
Bolotin S. V.
The problem of optimal control of a Chaplygin ball by internal rotors
2012, Vol. 8, No. 4, pp. 837-852
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.