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Department of Physics
Prof. R. Bundschuh
The Ohio State University
Seventh Problem Set for Physics 664 (Theoretical Mechanics)
Spring quarter 2004
Important dates:
May 31 no class, Jun 9 9:30am11:18am Fnal exam
Due date:
Thursday, May 20
17. Lagrangian for nonpotential force
12 points
As an example of a Lagrangian that does not correspond to motion under the in±uence of a
force that can be represented by a potential, let us study the Lagrangian
L
=
1
2
m
˙
~
r
2
+
q
c
˙
~
r
~
A
(
~
r
)

qφ
(
~
r
)
where
~
r
is the position of the particle in cartesian coordinates,
~
A
(
~
r
) is a vectorvalued function
of the coordinate,
φ
(
~
r
) is a scalar function of the coordinate, and
q
and
c
are constants.
a) Derive the three equations of motion corresponding to this Lagrangian.
b) Rewrite the equations of motion as a single vector equation using the curl of
~
A
(
~
r
) and
the gradient of
φ
(
~
r
).
c) Do you recognize these equations of motion?
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 Fall '04
 BUNDSCHUH
 mechanics

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