Dynamics Through First Order Differential Equations In The Configuration Space
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Dynamics through First-Order Differential Equations in the Configuration Space
The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field – the Cartesian vector field – given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.
Dynamics Through First-Order Differential Equations in the Configuration Space
The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field - the Cartesian vector field - given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.
Classical Mechanics And Electrodynamics (Second Edition)
Author: Jon Magne Leinaas
language: en
Publisher: World Scientific
Release Date: 2024-10-08
The book gives a general introduction to classical theoretical physics, in the fields of mechanics, relativity and electromagnetism. It is analytical in approach and detailed in the derivations of physical consequences from the fundamental principles in each of the fields. This second edition has a new part, namely Classical Field Theory. Highlighting a close connection between this part and earlier parts of the book, where particles, rather than fields are the center of attention.As a general introduction to classical theoretical physics, the book is different from most textbooks at this level, which focus either on classical mechanics or classical electrodynamics but not both. The book will in particular be useful as a textbook for physics courses with such a broader approach to classical physics. For a wider group of students, the book may be of interest for self study. The new inclusion on classical field theory, will give students greater understanding on previous parts of the book, such as examining the Lagrangian formulation of Maxwell's equations with Noether's theorem. This is central in the use of Lagrangian on fields, as also discussed.The text is illustrated with many figures, most of these in color. There are many useful examples and exercises which complement the derivations in the text.