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Classical Mechanics, Second Edition, 2nd Edition
book

Classical Mechanics, Second Edition, 2nd Edition

by Tai L. Chow
May 2013
Intermediate to advanced content levelIntermediate to advanced
639 pages
23h 12m
English
CRC Press
Content preview from Classical Mechanics, Second Edition, 2nd Edition
595
Appendix 3: Derivation of
Hamilton’s Principle from
D’Alembert’s Principle
We consider, for simplicity, a system of N particles of masses m
i
, located at the point r
i
and acted
upon by external forces F
i
. By D’Alembert’s principle, we have
()

Fmrr
ii
ii
i
N
−⋅=
=
δ
0
1
. (A3.1)
This is the dynamic condition to be satised by the impressed forces and the internal forces for arbi-
trary
δ
r
i
consistent with the constraints. We may interpret the virtual displacements
δ
r
i
as the small
variations in the following sense: a particle in its motion will take a certain path described by r=f(t)
under the action of external forces. Varied paths described i ...
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Publisher Resources

ISBN: 9781466569980