Skip to Main Content
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
110 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
Solution:
The problem possesses cylindrical symmetry, so we choose ρ, ϕ, and z as the generalized coordi-
nates, and we let the axis of the paraboloid correspond to the z-axis and the vertex of the parabo-
loid be located at the origin (Figure 4.11). The Lagrangian of the system is
LTVm
zm
gz=−=++−
1
2
2222
()

ρρϕ
where the reference level for the potential energy is set at the vertex of the paraboloid.
As ϕ is a cyclic coordinate, ∂L/∂ϕ = 0. Then, Lagrange’s equation for coordinate ϕ reduces to
d
d
d
dt
L
t
m
==
ϕ
ρϕ
()
2
0
from which we obtain
mρϕ
2
= constant
. (4.45)
Note that
mm
ρϕ
ρω
22
=
is just the angu ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Physics for Technology, Second Edition, 2nd Edition

Physics for Technology, Second Edition, 2nd Edition

Daniel H. Nichols
Engineering Mechanics

Engineering Mechanics

Dwarka Prasad Sharma
Engineering Physics

Engineering Physics

S. Mani Naidu
Mechanics

Mechanics

Somnath Datta

Publisher Resources

ISBN: 9781466569980