文档介绍：F. GANTMACHER
Lectures
in Analytical
Mechanics
TRANSLATED FROM THE RUSSIAN
BY E YANKOVSKY
MIR PUBLISHERS MOSCOW
ki3nATEJIbCTBO (tHAYKA*
MOCKBA
Contents
! Preface . ... ... ....
\chapter 1. THE' DIFFERE~TIALEQU~~ONS OF~.~OTIO~ OF AN
ARBITRARY SYSTEM OF PARTICLES . . . . . . . .
1. Free and Constrained Systems. Constraints and Their Classi-
fication ......................
2. Possible and Virtual Displacements. Ideal Constraints . . .
3. The General Equation of Dynamics. Lagrange's Equations
First published 1970 of the First Kind . . . . . . . . . . . . . . . . . .
Second printing 1975 4. The Principle of Virtual ~is~'Alernbertls Princi-
ple ................ .........
5. Holonomic Svstems. Independent ~
Forces . . . . . . . . . . . . . . . . . . . . . . .
6. Lagrange's Equations of the Second Kind in Independent
Coordinates . . . . . . . . . . . . . . . . . . . . . .
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''orces . . . . . . . . . . . . . . . .
programme of the Joint Indo-Soviet Board 9. Electromechanica! Analogies . . . . . . . . . . . . .
to make the best Soviet textbooks 10. Appell's Equations for ~onholonomicSystems. ~seudocoordi-
available for Indian students nates . . . . . . . .l . . . . . . . . . . . . . . . . .
'\Chapter 2. THE EQUATIONS OF MOTION IN A POTENTIAL 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 . . . . . . . . . . . . . . . . . .
Chapter 3. VARIATIONAL PRINCI