Department of Physics
Prof. R. Bundschuh
The Ohio State University
Sixth Problem Set for Physics 664 (Theoretical Mechanics)
Spring quarter 2004
Important dates:
May 11 9:30am10:18am midterm exam,
May 31 no class, Jun 9 9:30am11:18am Fnal exam
Due date:
Thursday, May 13
15. Particle on a helix
9 points
A particle of mass
m
moves under the in±uence of gravity along the helix
z
=
kθ
,
r
= constant,
where
k
is a constant and the
z
axis points vertically upwards.
a) Write down the Lagrangian of the system expressing it in the variable
z
.
b) Calculate the generalized momentum
p
z
.
c) Calculate the Hamiltonian in terms of the variables
z
and
p
z
.
d) Derive the Hamiltonian equations of motion of the system.
e) Solve the Hamiltonian equations of motion.
16. Hamiltonians and energy
22 points
In this problem we want to develop a feeling for the relationship between the Hamiltonian
and the total energy of a system and their conservation. To this end, write down the kinetic
energy, the potential energy, the total energy, the Lagrangian, the generalized momenta, and
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This note was uploaded on 07/17/2008 for the course PHYS 664 taught by Professor Bundschuh during the Fall '04 term at Ohio State.
 Fall '04
 BUNDSCHUH
 mechanics

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