Cornelius Lanczos.
The Variational Principles of Mechanics: 4th edn.
Dover. 1970
Analytical mechanics is, of course, a topic of perennial interest and usefulness
in physics and engineering, a discipline that boasts not only many practical applications,
but much inherent mathematical beauty.
Unlike many standard textbooks on advanced mechanics, however,
the present text eschews a primarily technical and formalistic treatment
in favor of a fundamental, historical, philosophical approach.
As the author remarks, there is a “tremendous treasure of philosophical meaning”
behind the great theories of Euler and Lagrange, Hamilton,
Jacobi and other mathematical thinkers.
Well-written, authoritative and scholarly, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, Lagrange and Hamilton. After a philosophical evaluation of the variational approach, the text is divided into 11 chapters:
I. The Basic Concepts of Analytical Mechanics
II. The Calculus of Variations
III. The Principle of Virtual Work
IV. D’Alembert’s Principle
V. The Lagrangian Equations of Motion
VI. The Canonical Equations of Motion
VII. Canonical Transformations
VIII. The Partial Differential Equation of Hamilton-Jacobi
IX. Relativistic Mechanics
X. Historical Survey
XI. Mechanics of the Continua