University of Alabama in Huntsville
Department of Physics
Fall 2008
PH 601: Classical Dynamics I
Homework Problem Set No. 2
Deadline: 10 September, 2008
Problem 6:
Let the Lagrangian be
L=−mc2s1−
˙q2
c2
−eφ(q, t) + e
c
3
X
i=1
Ai(q, t) ˙qi.
Show that this Lagrangian describes the motion of a relativistic particle of
mass mand charge emoving in an electromagnetic field described by the
potentials φ, A. What is the slow motion limit?
Problem 7:
1. One may formulate a theory in which the “Lagrangian” ˜
Lmay include
higher derivatives of the generalized coordinates. What are the equa-
tions of motion for a “Lagrangian” of the form ˜
L=˜
L(q, ˙q, ¨q;t)?
2. Let ˜
L(q, ˙q, ¨q;t) = −
1
2q¨q−
1
2kq2. What are the equations of motion?
What kind of motion does this “Lagrangian” describe?
Problem 8:
Let the Lagrangian L=eγt (1
2m˙q2
−
1
2kq2), where m, k , γ are constants.
1. What are the equations of motion? What kind of motion does this
Lagrangian describe? What are the system’s constants of motion (if
any)?
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