Ebook: Dynamics of Synchronising Systems

This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretation and are valid for a broad class of weak-interaction problems in mechanics. The criteria of stability regarding stationary solutions of these equations are derived explicitly and correspond to the extremum of a special "potential" function. Much consideration is given to applications in vibrational technology, electrical engineering and quantum mechanics, and a number of results are presented that are immediately useful in engineering practice. The book is intended for mechanical engineers, physicists, as well as applied mathematicians specializing in the field of ordinary differential equations.

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This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretation and are valid for a broad class of weak-interaction problems in mechanics. The criteria of stability regarding stationary solutions of these equations are derived explicitly and correspond to the extremum of a special "potential" function. Much consideration is given to applications in vibrational technology, electrical engineering and quantum mechanics, and a number of results are presented that are immediately useful in engineering practice. The book is intended for mechanical engineers, physicists, as well as applied mathematicians specializing in the field of ordinary differential equations.

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This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretation and are valid for a broad class of weak-interaction problems in mechanics. The criteria of stability regarding stationary solutions of these equations are derived explicitly and correspond to the extremum of a special "potential" function. Much consideration is given to applications in vibrational technology, electrical engineering and quantum mechanics, and a number of results are presented that are immediately useful in engineering practice. The book is intended for mechanical engineers, physicists, as well as applied mathematicians specializing in the field of ordinary differential equations.
Content:
Front Matter....Pages i-10
Locally integrable dynamical systems....Pages 11-33
Conservative dynamical systems....Pages 35-47
Dynamical systems in a plane....Pages 49-80
Conservative systems with many degrees of freedom....Pages 81-112
Resonant solutions for systems integrable in generating approximation....Pages 113-155
Canonical averaging of the equations of quantum mechanics....Pages 157-188
The problem of weak interaction of dynamical objects....Pages 189-196
Synchronisation of anisochronous objects with a single degree of freedom....Pages 197-233
Synchronisation of inertial vibration exciters....Pages 235-266
Synchronisation of dynamical objects of the general type....Pages 267-286
Periodic solutions in problems of excitation of mechanical oscillations....Pages 287-316
Back Matter....Pages 317-329

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This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretation and are valid for a broad class of weak-interaction problems in mechanics. The criteria of stability regarding stationary solutions of these equations are derived explicitly and correspond to the extremum of a special "potential" function. Much consideration is given to applications in vibrational technology, electrical engineering and quantum mechanics, and a number of results are presented that are immediately useful in engineering practice. The book is intended for mechanical engineers, physicists, as well as applied mathematicians specializing in the field of ordinary differential equations.
Content:
Front Matter....Pages i-10
Locally integrable dynamical systems....Pages 11-33
Conservative dynamical systems....Pages 35-47
Dynamical systems in a plane....Pages 49-80
Conservative systems with many degrees of freedom....Pages 81-112
Resonant solutions for systems integrable in generating approximation....Pages 113-155
Canonical averaging of the equations of quantum mechanics....Pages 157-188
The problem of weak interaction of dynamical objects....Pages 189-196
Synchronisation of anisochronous objects with a single degree of freedom....Pages 197-233
Synchronisation of inertial vibration exciters....Pages 235-266
Synchronisation of dynamical objects of the general type....Pages 267-286
Periodic solutions in problems of excitation of mechanical oscillations....Pages 287-316
Back Matter....Pages 317-329
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