Gantmacher F. Lectures in Analytical Mechanics

Translated from Russian by George Yankovsky. — Moscow: Mir, 1975. — 264 p.The present text does not claim to cover fully the material of analytical mechanics. It developed out of a course of lectures given by the author over a period of six years in the Moscow Physico-Technical Institute. This circumstance determined the choice of material and the manner of its presentation.
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, 4 and 7). Following the ideas of Poincare and Gartan, 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.
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.