文档介绍：F. GANTMACHER
Lectures
in Analytical
Mechanics
TRANSLATED FROM THE RUSSIAN
BY E YANKOVSKY
MIR PUBLISHERS MOSCOW
Contents
r Preface . ....
\chapter 1. THE- ~IFFE~EN'T~~L'EQUAT~O~~OF~~OTIO~ OF AN
ARBITRARY SYSTEM OF PARTICLES . . . . . . . .
1. Free and Constrained Systems. Constraints and Their Classi-
fication . . . . . . . . . . . . . . . . . . . . . .
2. Possible and Virtual Displacements. ~dsaiConstraints . . ,
3. The General Equation of Dynamics. Lagrange's Equations
First published 1970 of the First ~ind. . . . . . . . . . . . . . . . . .
Second printing 1975 4. The Principlo of Virtual Dispj-acements. D9Alembert's Princi-
ple ................ .........
5. Holonomic Systems. Independent ~oorhinates. Generalized
Forces . . . . . . . . .. . . . . . . . . . . . . . .
6. Lagrange's Equations o£ the Second Kind in Independent
Coordiiates . - . . . . . . . . . . . . . . . . . . . . .
This book has been mended for 7. Investigating Lagrange's Equations . . . . . . . . . . .
publication by Indian specialists under the 8. Theorem on Variation of Total Energy. Potential, Gyroscopic
and Dissipative 1'4 orces . . . . . . . . . . . . . . . .
programme of the Joint Indo-Soviet Board 9. Electromeclianica! Analogies . . . . . . . . . . . . . .
to make the best Soviet textbooks 10. Appell's Equations for ~onholonomicSystems. Pseudocoordi-
available for Indian students nates . . . . . . . .I . . . . . . . . . . . . . . . . .
'\Chapter 2. THE EQUATIONS OF MOTION IN A POTEYTIAL, FIELD
11. Lagrange's Equations for Potential Forces. The Generalized
Potential . Nonnatural Systems . . . . . . . . . . . . .
12. Canonical Equations of Hamilton . . . . . . . . . . . .
13. Routh's Equations . . . . . . . . . . . . . . . . . . .
14. Cyclic Coordinates . . . . . . . . . . . . . . . . . . .
15. The Poisson Bracket . . . . . . . . . . . . . . . . . .
x Chapter 3. VARIATIONAL PRINCIPLES AND INT