Gantmacher - Lectures in Analytical Mechanics torrent

Lectures on Analytical Mechanics by F. Gantmacher.


The course of analytical mechanics is a foundation supporting such
divisions of theoretical physics as quantum mechanics, the special
and general theories of relativity, and so forth. For this reason, a
detailed presentation is given of variational principles and the
integral invariants of mechanics, canonical transformations, the
Hamilton-Jacobi equation, and systems with cyclic (ignorable)
coordinates (Chapters 2, 3, 4and 7). Following the ideas of Poincare
and Cartan, the author takes the integral invariants of mechanics as
the basis of presentation. Here they do not represent an
embellishment of the theory but its actual workaday machinery. The
technical applications are associated with a consideration of
constrained systems, which are studied in detail in Chapter 1. In a
special section of that chapter, which is devoted to
electromechanical analogies, the possibility is investigated of
extending the analytical methods of mechanics to electrical and
electromechanical systems. In Chapters 5 and 6 are given
applications of analytical mechanics to Lyapunov's theory of
stability and the theory of oscillations. Elements of modern
frequency methods are given along with the classical problems in the
theory of linear oscillations. Problems in the dynamics of rigid
bodies are taken up in individual examples.

Whom this text is for and what are the prerequisites?

It is assumed the reader is acquainted with the general fundamentals
of theoretical mechanics and higher mathematics. The text is
designed for undergraduate and graduate students of
mechanico-mathematical, physical and physical-engineering
departments of universities, and also for research engineers and
other specialists who feel a need to extend and deepen their
knowledge in the field of mechanics.

This book was translated from the Russian by George Yankovsky and
was first published by Mir Publishers in 1975.

All credits to the original uploader.


DJVU | 2.9 MB | OCR | Pages: 265 | Cover |

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Contents
Preface 7

Chapter 1
The Differential Equatlons Of Motion Of An Arbitrary System Of

Chapter 2.
The Equations Of Motion In A Potential Field 66

Chapter3.
Variational Principles And Integral Invariants 88

Chapter4.
Canonical Transformations And The Hamilton-Jacobi Equation 128

Chapter5.
Stability Of Equilibrium And The Motions Of A System 166

Chapter6.
Small Oscillations 202

Chapter7.
Systems With Cyclic Coordinates 242


References 259
Name Index 260
Subject Index 261