Constrained dynamics of rolling balls and moving atoms
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This dissertation is devoted to the study of the dynamics, conservation laws and symmetries of rolling spheres, with special attention to applications to atomic and molecular systems. Previously known conservation laws of the rolling motion are associated with the nonholonomic version of Noether's theorem. Moreover, the conservation laws are related to the reduction by Lie symmetries of the dynamic equations of motion. Symmetries in the Noether's theorem and in the reduction by Lie symmetries are compared in their applications. In addition, we analyze the collective motion of the system of rolling ...