Geodesic
The problem of optimal control of a Chaplygin ball by internal rotors
Russian journal of nonlinear dynamics, Tome 8 (2012) no. 4, pp. 837-852

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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. 
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     author = {Sergey V. Bolotin},
     title = {The problem of optimal control of a {Chaplygin} ball by internal rotors},
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     url = {http://geodesic.mathdoc.fr/item/ND_2012_8_4_a10/}
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Sergey V. Bolotin. The problem of optimal control of a Chaplygin ball by internal rotors. Russian journal of nonlinear dynamics, Tome 8 (2012) no. 4, pp. 837-852. http://geodesic.mathdoc.fr/item/ND_2012_8_4_a10/