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Physics 110, Problem set #4
Due April 28, 2010
1.
A pendulum is suspended from the edge of a rotating disk, as shown.
a.
Using
(
?
,
±
,
²
)
as the generalized coordinates, write down the Lagrangian
of the system (10 pts). Note that
±
is measured from the projection of
²
,
as shown.
b.
What are the conserved quantities? There are at least two (6 pts).
c.
Find three equations of motion for the system (6 pts).
*This problem is not hard at all with Mathematica.*
`
2.
Constraints (25 pts): A bead with (mass
m
) is constrained to move along a stiff
parabolic wire described by
α
y
z
=
on the
yz
plane, as shown.
a.
Write down the Lagrangian of the system, using
z
y
x
,
,
as the generalized
coordinates (2 pts).
b.
What are the 2 constraint equations? Express them in the form of
0
;
0
2
1
=
=
G
G
(2 pts).
c.
Find the equations of motion for
z
y
x
,
,
, and the Lagrange multiplier(s) (4
pts).
d.
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This note was uploaded on 02/01/2011 for the course MATH 171 taught by Professor R during the Spring '09 term at Stanford.
 Spring '09
 R

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