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| Author | : Vladimir Igorevich Arnolʹd |
| Publisher | : Addison-Wesley Longman |
| Total Pages | : 286 |
| Release | : 1989-01-01 |
| Genre | : Science |
| ISBN | : 9780201094060 |
| Author | : V. I. Arnold |
| Publisher | : |
| Total Pages | : 286 |
| Release | : 1979 |
| Genre | : Ergodic theory |
| ISBN | : |
| Author | : Vladimir Igorevich Arnolʹd |
| Publisher | : |
| Total Pages | : 312 |
| Release | : 1968 |
| Genre | : Dynamics |
| ISBN | : |
| Author | : V.I. Arnol'd |
| Publisher | : Springer Science & Business Media |
| Total 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.
| Author | : V.I. Arnol'd |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 552 |
| Release | : 1997-09-05 |
| Genre | : Mathematics |
| ISBN | : 9780387968902 |
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.
| Author | : R. Jancel |
| Publisher | : Elsevier |
| Total Pages | : 441 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 1483186261 |
Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.
| Author | : G. L. Kotkin |
| Publisher | : Elsevier |
| Total Pages | : 288 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 148318661X |
Collection of Problems in Classical Mechanics presents a set of problems and solutions in physics, particularly those involving mechanics. The coverage of the book includes 13 topics relevant to classical mechanics, such as integration of one-dimensional equations of motion; the Hamiltonian equations of motion; and adiabatic invariants. The book will be of great use to physics students studying classical mechanics.
| Author | : Vladimir I. Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 664 |
| Release | : 2004-06-24 |
| Genre | : Mathematics |
| ISBN | : 9783540206149 |
Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
| Author | : V. I. Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 469 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1475716931 |
Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.
| Author | : O. L. de Lange |
| Publisher | : OUP Oxford |
| Total Pages | : 608 |
| Release | : 2010-05-06 |
| Genre | : Science |
| ISBN | : 0191582867 |
Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation and rotation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain and analyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and to study the effects of changing parameters. The book will be useful to students and lecturers in undergraduate and graduate courses on classical mechanics, and students and lecturers in courses in computational physics.
