Synopsis
Explore the core ideas of dynamical systems with clear, accessible explanations.
Dynamical Systems presents a structured introduction to how physical and mathematical systems evolve over time. It surveys existence theorems, variational principles, stability, and the geometry of motion, from basic setup to the edges of current theory. The book blends foundational concepts with key results and methods, guiding readers through both classic problems and modern perspectives.
With a focus on two- and multi-degree-of-freedom systems, you’ll see how energy, momentum, and other invariants shape motion. The text weaves together formal methods, geometric ideas, and concrete examples, including the famous three-body problem and the role of Poincaré’s geometric theorem in understanding complex dynamics.
- Foundational setup: how differential equations describe evolving states in physical systems
- Variational principles and their applications to motion and energy
- Stability, periodic motions, and the structure of motion in two and more degrees of freedom
- The three-body problem and related geometric methods for predicting behavior
Ideal for readers of advanced undergraduate to graduate level mathematics and physics who want a rigorous, approachable path into dynamical systems.
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Présentation de l'éditeur
Excerpt from Dynamical Systems
Normal form for completely stable systems. Proof of the lemma of section 5 Reversibility and complete stability Other types of stability.
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.
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Dynamical Systems (Classic Reprint)
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Paperback. Etat : New. Print on Demand. This book delves into the fascinating world of dynamical systems, exploring the mathematical and physical principles that govern the motion of objects. The author, drawing on his own groundbreaking research and inspired by the work of luminaries like Galileo, Newton, and PoincarÃÂ , examines the essential role of differential equations in understanding dynamic phenomena. The text delves into the fundamental concepts of energy conservation, variational principles, and stability of motion, providing a comprehensive framework for analyzing the behavior of complex systems. Through discussions of Lagrangian systems, geometric constraints, and the principle of least action, the book offers a deep exploration of the mathematical elegance and physical significance of dynamical systems. By examining the nature of forces and their impact on motion, the author sheds light on the intricacies of motion in both conservative and dissipative systems, ultimately demonstrating the power of mathematics to illuminate the intricate workings of the physical world. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781334016653_0
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Paperback. Etat : Brand New. 311 pages. 9.00x6.00x0.60 inches. This item is printed on demand. N° de réf. du vendeur zk1334016658
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Dynamical Systems (Classic Reprint)
Edité par
Forgotten Books Apr 2018, 2018
ISBN 10 : 1334016658
ISBN 13 : 9781334016653
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