Mathematical Methods Of Classical Mechanics

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 9781475720631
Size: 17.44 MB
Format: PDF
View: 77

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.

Mathematical Methods Of Classical Mechanics

Author: V. I. Arnold
Publisher: Springer Science & Business Media
ISBN: 9781475716931
Size: 13.71 MB
Format: PDF, ePub, Mobi
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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.

Mathematical Methods Of Classical Mechanics

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 0387968903
Size: 13.51 MB
Format: PDF, ePub, Mobi
View: 66

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.

Foundations Of Mechanics

Author: Ralph Abraham
Publisher: American Mathematical Soc.
ISBN: 9780821844380
Size: 14.54 MB
Format: PDF, ePub, Mobi
View: 90

Undoubtedly [the book] will be for years the standard reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics. --Zentralblatt fur Mathematik For many years, this book has been viewed as a classic treatment of geometric mechanics. It is known for its broad exposition of the subject, with many features that cannot be found elsewhere. The book is recommended as a textbook and as a basic reference work for the foundations of differentiable and Hamiltonian dynamics.

Nonholonomic Mechanics And Control

Author: A.M. Bloch
Publisher: Springer Science & Business Media
ISBN: 9780387955353
Size: 17.38 MB
Format: PDF, Mobi
View: 97

This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.

Essays In Mathematics And Its Applications

Author: Themistocles Rassias
Publisher: Springer
ISBN: 9783319313382
Size: 15.30 MB
Format: PDF, Docs
View: 19

This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.