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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
95Lagrangian Formulation of Mechanics
© 2010 Taylor & Francis Group, LLC
and the potential energy is
V = mg(l lcos θ) = mgl(1 − cos θ).
Then the Lagrangian L is
LTVmlmgl=−=−
1
2
1
22
θθ
(cos )
and the Lagrange’s equation is
d
d
/
t
LL
gl
=+ =

θ
θ
θθ
()si
n0
.
For a small angle of oscillation, sin θ θ, the Lagrange’s equation of motion reduces to the
familiar harmonic oscillator type of equation

θθ+=
()gl
/0
.
Example 4.2
A bead slides on a smooth wire that is rotating uniformly about a point O in a horizontal plane (the
xy-plane). Describe the motion of the bead (Figure 4.5).
θ
l
m
O
FIGURE 4.4 Simple pendulum.
Bead
Wire
O
x
ω
θ
r
y
FIGURE 4.5 A bead slides on a ...
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Publisher Resources

ISBN: 9781466569980