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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
130 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
or, simply,
H = E = T + V = p
2
/2m+ kx
2
/2.
Hamilton’s equations give
∂∂==−∂ ∂= =∂∂=
Hp pm xHxkxp Ht//
//
,a
nd
0
.
The first equation is the definition of momentum; the second equation is the equation of motion
mx kx

+=0
,
and the last equation is the statement of conservation of energy.
Example 5.2
A particle of mass m is attracted to a fixed point O by an inverse square force FGMr kr
r
=− =−
//
22
(Figure 5.1). Solve this problem using Hamilton’s equations.
Solution:
As shown in Figure 5.1, we use plane polar coordinates (r, θ). The velocity of the particle is given
by
vrere
r
=+
ˆˆ
θ
θ
.
Hence,
Tmrr
=+
1
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Publisher Resources

ISBN: 9781466569980