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| Author | : Darryl D. Holm |
| Publisher | : Oxford University Press |
| Total Pages | : 537 |
| Release | : 2009-07-30 |
| Genre | : Mathematics |
| ISBN | : 0199212902 |
A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject.
| Author | : Richard Talman |
| Publisher | : John Wiley & Sons |
| Total Pages | : 582 |
| Release | : 2008-07-11 |
| Genre | : Science |
| ISBN | : 3527617817 |
Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.
| Author | : Waldyr Muniz Oliva |
| Publisher | : Springer |
| Total Pages | : 277 |
| Release | : 2004-10-23 |
| Genre | : Science |
| ISBN | : 354045795X |
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
| Author | : Jared Maruskin |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 348 |
| Release | : 2018-08-21 |
| Genre | : Science |
| ISBN | : 3110597802 |
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
| Author | : Francesco Bullo |
| Publisher | : Springer |
| Total Pages | : 727 |
| Release | : 2019-06-12 |
| Genre | : Science |
| ISBN | : 1489972765 |
The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
| Author | : Ovidiu Calin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2006-03-15 |
| Genre | : Mathematics |
| ISBN | : 0817644210 |
* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
| Author | : Dariusz Chruscinski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0817681760 |
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
| Author | : G. Giachetta |
| Publisher | : World Scientific |
| Total Pages | : 405 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 9814313726 |
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.
| Author | : Velimir Jurdjevic |
| Publisher | : Cambridge University Press |
| Total Pages | : 516 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0521495024 |
Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
| Author | : Waldyr M. Oliva |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 292 |
| Release | : 2002-10-23 |
| Genre | : Mathematics |
| ISBN | : 9783540442424 |
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
