Constrained dynamics of rolling balls and moving atoms.

摘要

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 particles for its statistical quantities under the constraint condition of rolling without slipping motion. The numerical simulations revealed some of qualitative characteristics in the statistical mechanics of the rolling-constrained system.;As a separate topic, the study of the molecular dynamics is discussed in relation to the results of recent experimental achievements with the non-contact atomic force microscopy. We propose a novel scenario explaining the process of single-atom manipulation in terms of the classical resonance effect.