A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Classic Reprint): With an Introduction to the Problem of Three Bodies - Couverture souple

E. T. Whittaker

Couverture souple

ISBN 10 : 1440089477 ISBN 13 : 9781440089473

Editeur : Forgotten Books, 2018

Synopsis

Mastering the laws that govern motion across particles and rigid bodies. This authoritative work covers the full landscape of analytical dynamics, from fundamental principles to advanced methods, with a clear path toward solving complex problems like the three-body system.

The book presents a rigorous framework for dynamics, including the equations of motion, energy and momentum concepts, and the powerful tools of Lagrangian and Hamiltonian formalisms. It explores how motion can be reduced, transformed, and analyzed through variational principles, integrals of motion, and transformation theory. With detailed treatments of rigid dynamics and vibrational analysis, it guides readers from basic ideas to sophisticated applications in physics, engineering, and applied mathematics.

• Foundations of motion: holonomic and non-holonomic systems, constraints, and the role of energy and potential functions.


• Advanced methods: Lagrange and Hamilton formalisms, canonical transformations, and integral invariants.


• Special topics: dynamics of rigid bodies, moments of inertia, Euler angles, Poisson brackets, and transformation theory.


• Problem-solving strategies: reduction of complex problems, such as the three-body problem, and analysis of vibrational systems.

Ideal for readers who seek a deep, mathematically grounded treatment of dynamics, from graduate students to researchers in physics and applied mathematics, as well as engineers needing a solid theoretical backbone.

A propos du livre

Présentation de l'éditeur

Excerpt from A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies

In revising this book for a second edition, I have endeavoured to give references to, and in some cases accounts of, the numerous original researches in Dynamics which have been published by various investigators since the first edition appeared. I have moreover added some historical matter, and rewritten many sections. It is not necessary to specify these in detail, but perhaps I may mention that the new explanation of the transformation-theory of Dynamics in 125 sprang from a desire to do justice to the earliest great work of Hamilton's genius: that the changes in 69 (the motion of a body about a fixed point under no forces) arose from my opinion that the Jacobian functions are preferable to the Weierstrassian in the numerical computations: and that I should have liked to give a fuller proof of Sundman's theorem (181), but thought it better to give only such an account as might impel the reader to consult Mr Sundman's own accessible and readable memoir.

I wish again to record my obligations to the staff of the Cambridge University Press.

About the Publisher

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1440089477
• ISBN 13: 9781440089473
• Reliure: Broché
• Nombre de pages: 448
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