Classical Dynamics of Particles and Systems
Title | Classical Dynamics of Particles and Systems PDF eBook |
Author | Jerry B. Marion |
Publisher | Academic Press |
Pages | 593 |
Release | 2013-10-22 |
Genre | Science |
ISBN | 1483272818 |
Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handling both the formalism of the theory and the operational technique of problem solving. Vector methods are developed in the first two chapters and are used throughout the book. Other chapters cover the fundamentals of Newtonian mechanics, the special theory of relativity, gravitational attraction and potentials, oscillatory motion, Lagrangian and Hamiltonian dynamics, central-force motion, two-particle collisions, and the wave equation.
Mathematical Methods of Classical Mechanics
Title | Mathematical Methods of Classical Mechanics PDF eBook |
Author | V.I. Arnol'd |
Publisher | Springer Science & Business Media |
Pages | 530 |
Release | 2013-04-09 |
Genre | Mathematics |
ISBN | 1475720637 |
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Dynamical Systems in Classical Mechanics
Title | Dynamical Systems in Classical Mechanics PDF eBook |
Author | Valeriĭ Viktorovich Kozlov |
Publisher | American Mathematical Soc. |
Pages | 268 |
Release | 1995 |
Genre | Mathematics |
ISBN | 9780821804278 |
This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include... the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics.
Structure of Dynamical Systems
Title | Structure of Dynamical Systems PDF eBook |
Author | J.M. Souriau |
Publisher | Springer Science & Business Media |
Pages | 427 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461202817 |
The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.
Dynamical Systems and Geometric Mechanics
Title | Dynamical Systems and Geometric Mechanics PDF eBook |
Author | Jared Maruskin |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 350 |
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.
Mechanics and Dynamical Systems with Mathematica®
Title | Mechanics and Dynamical Systems with Mathematica® PDF eBook |
Author | Nicola Bellomo |
Publisher | Springer Science & Business Media |
Pages | 427 |
Release | 2012-12-06 |
Genre | Technology & Engineering |
ISBN | 146121338X |
Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa tions is a relevant, maybe the fundamental, aspect of the interactions be tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization.
Classical Dynamics
Title | Classical Dynamics PDF eBook |
Author | Jorge V. José |
Publisher | Cambridge University Press |
Pages | 702 |
Release | 1998-08-13 |
Genre | Science |
ISBN | 9780521636360 |
A comprehensive graduate-level textbook on classical dynamics with many worked examples and over 200 homework exercises, first published in 1998.