Analytical Mechanics

ISBN-13: 9783642536502 / Angielski / Miękka / 2014 / 864 str.

A.I. Lurie;A. BELYAEV

Opis

According to established tradition, courses on analytical mechanics include general equations of motion of holonomic and non-holonomic systems, vari ational principles, theory of canonical transformations, canonical equations and theory of their integration (the Hamilton-Jacobi theorem), integral in variants, theory of last multiplier and others. The fundamental laws of mechanics are taken for granted and are not subject to discussion. The present book is concerned with those issues of the above listed sub jects which, in the author's opinion, are most closely related to engineering problems. Application of the methods of analytical mechanics to non-trivial prob lems at the very stage of constructing the equations requires detailed knowl edge of the issues that are normally only briefly touched upon. With this perspective considerable attention is paid to ways of introducing the gener alised coordinates, the theory of finite rotation, methods of calculating the kinetic energy, the energy of accelerations, the potential energy of forces of various nature, and the resisting forces. These introductory chapters, which have to some extent independent significance, are followed by those on methods of constructing differential equations of motion for holonomic and non-holonomic systems in various forms. In these chapters the issues of their interrelations, determination of the constraint forces and some prob lems of analytical statics are discussed as well. It is thought useful to include geometric considerations of the motion of a material system as motion of the representative point in Riemannian space."

Recenzje

From the reviews:

"This monumental treatise on analytical mechanics is a translation of the original Russian edition from 1961. ... it contains a wealth of material on the classic theory of mechanics, and methods of formulating the equations of motion of mechanical systems. ... This book ... makes good background reading for anyone with an interest in the classical foundations of mechanics. The gradual build up to the general equations and principles, supplemented with many examples, prepares the reader well ... ." (Steen Krenk, Journal of Vibration and Acoustics, April, 2004)

"This book is a translation of a book originally printed in Russian in 1961. It offers a treatment of the dynamics of mechanical systems. ... Analytical Mechanics would be a useful reference book for a person who is interested in engineering dynamics. It could also serve as a textbook for a graduate course in engineering dynamics ... ." (Richard H. Rand, SIAM Review, Vol. 45 (2), 2003)

"This textbook ... represents the lectures of a late great scholar and teacher at the Saint-Petersburg Polytechnic Institute. ... the work is of original conception and contains also original contributions of the author. ... A great attention is paid to the statement of problems and to the construction of the corresponding equations of motion. The book could be of interest to a large circle of graduate students as well as to researchers in the field who wish to acquire a deeper insight into analytical mechanics." (P. Teodorescu, Zentralblatt MATH, Vol. 1015, 2003)

Spis treści

1 Basic definitions.- 2 Rigid body kinematics — basic knowledge.- 3 Theory of finite rotations of rigid bodies.- 4 Basic dynamic quantities.- 5 Work and potential energy.- 6 The fundamental equation of dynamics. Analytical statics.- 7 Lagrange’s differential equations.- 8 Other forms of differential equations of motion.- 9 Dynamics of relative motion.- 10 Canonical equations and Jacobi’s theorem.- 11 Perturbation theory.- 12 Variational principles in mechanics.- A Elements of the theory of matrices.- A.1 Definitions.- A.2 Operations on matrices.- A.3 Inverse of the matrix.- A.4 Matrix representation of the operations of vector calculus.- A.5 Differentiation of a matrix.- B Basics of tensor calculus.- B.1 General non-orthogonal coordinates.- B.2 Vectors using the non-orthogonal coordinates.- B.3 Tensors of second rank in the non-orthogonal coordinates.- B.4 Curvilinear coordinates.- B.5 Covariant differentiation.- B.6 Examples of non-orthogonal curvilinear coordinates.- B.7 Formulae of the theory of surfaces.- B.8 Curvature of lines on the surface.- B.9 Covariant derivative of a vector on the surface.- B.10 Orthogonal curvilinear coordinates.- B.11 Finite-dimensional Euclidean space.- B.14 The Riemann-Christoffel tensor.- References.

Blurb

This is a translation of A.I. Lurie classical Russian textbook on analytical mechanics. Part of it is based on courses formerly held by the author. It offers a consummate exposition of the subject of analytical mechanics through a deep analysis of its most fundamental concepts. The book has served as a desk text for at least two generations of researchers working in those fields where the Soviet Union accomplished the greatest technological breakthrough of the XX century - a race into space. Those and other related fields continue to be intensively explored since then, and the book clearly demonstrates how the fundamental concepts of mechanics work in the context of up-to-date engineering problems. This book will help researchers and graduate students to acquire a deeper insight into analytical mechanics.