Name:Solutions
PHY 5246: Theoretical Dynamics, Fall 2012
November 5th, 2012
Midterm Exam # 2
Always remember to write full work for what you do. This will help your grade in
case of incomplete or wron
Name: SOLUTIONS
PHY 5246: Theoretical Dynamics, Fall 2012
October 1st, 2012
Midterm Exam # 1
Always remember to write full work for what you do. This will help your grade in
case of incomplete or wron
PHY 5246: Theoretical Dynamics, Fall 2012
December 5th, 2012
Assignment # 11, Solutions
1
Graded problems
Problem 1 (Goldstein 9.21)
(1.a)
We have a 1D system
H=
1
p2
2.
2
2q
D=
pq
Ht
2
We want to s
PHY 5246: Theoretical Dynamics, Fall 2012
November 21st, 2012
Assignment # 10, Solutions
1
Graded problems
Problem 1
(1.a)
The Lagrangian is
1
L = m(r 2 + r 2 2 + r 2 sin2 2 ) V (r ),
2
and the conjug
PHY 5246: Theoretical Dynamics, Fall 2012
November 28th, 2012
Assignment # 11
(Graded problems are due Wednesday December 5th, 2012)
1
Graded problems
1. Chapter 9, Problem 21 of your book.
2. Chapter
PHY 5246: Theoretical Dynamics, Fall 2012
Assignment # 8, Solutions
1
Graded Problems
Problem 1
First we calculate the moments of inertia:
I1 = I2 = m
x3
I3 =
a
x1
ma2
.
2
(1.a)
The torque is zero! Th
PHY 5246: Theoretical Dynamics, Fall 2012
November 16th, 2012
Assignment # 10
(Graded problems are due Wednesday November 28th, 2012)
1
Graded problems
1. Consider a particle in a central force eld.
(
PHY 5246: Theoretical Dynamics, Fall 2012
Assignment # 7, Solutions
1
Graded Problems
Problem 1
(1.a)
In order to nd the equation of motion of the triangle,
we need to write the Lagrangian, with gener
PHY 5246: Theoretical Dynamics, Fall 2012
November 7th , 2012
Assignment # 9
(Graded problems are due Friday November 16th , 2012)
1
Graded problems
1. Determine the eigenfrequencies and describe the
PHY 5246: Theoretical Dynamics, Fall 2012
October 24th , 2012
Assignment # 8
(Graded problems are due Wednesday October 31st , 2012)
1
Graded problems
1. A uniform solid cylinder of mass m, length b,
PHY 5246: Theoretical Dynamics, Fall 2012
Assignment # 6, Solutions
1
Graded Problems
Problem 1
The equation of the orbit for the force given in this problem is
2
2
that can be written as
1
mr 2
mk m
PHY 5246: Theoretical Dynamics, Fall 2010
Assignment # 4, Solutions
1
Graded Problems
Problem 1
(1.a)
The problem has spherical symmetry and is therefore naturally solved using spherical coordinates
(
PHY 5246: Theoretical Dynamics, Fall 2012
October 10th , 2012
Assignment # 6
(Graded problems are due Wednesday October 17st , 2012)
1
Graded problems
1. Discuss the motion of a particle in a central
PHY 5246: Theoretical Dynamics, Fall 2012
Assignment # 5, Solutions
1
Graded Problems
Problem 1
(1.a)
Using the equation of the orbit or force law
d2
d2
1
mr 2
1
+ = 2 F (r ) ,
r
r
l
(1)
with r () = k
PHY 5246: Theoretical Dynamics, Fall 2012
October 17th , 2012
Assignment # 7
(Graded problems are due Wednesday October 24th , 2012)
1
Graded problems
1. Find the frequency of small oscillations for a
PHY 5246: Theoretical Dynamics, Fall 2012
September 26th , 2012
Assignment # 5
(Graded problems are due Wednesday October 10th , 2012)
1
Graded problems
1. Consider a particle that moves in a logarith
PHY 5246: Theoretical Dynamics, Fall 2012
Assignment # 3, Solutions
1
Graded Problems
Problem 1
(1.a)
We use cylindrical coordinates and notice that z = r cot . We use cfw_r, as generalized coordinat
PHY 5246: Theoretical Dynamics, Fall 2012
Assignment # 2, Solutions
1
Graded Problems
Problem 1
(1.a)
The coordinates can be written using spherical coordinates as:
x = R sin cos(t) ,
y = R sin sin(t)
PHY 5246: Theoretical Dynamics, Fall 2012
September 19th , 2012
Assignment # 4
(Graded problems are due Wednesday September 26th , 2012)
1
Graded problems
1. A spherical pendulum consists of a bob of
PHY 5246: Theoretical Dynamics, Fall 2012
September 12th , 2012
Assignment # 3
(Graded problems are due Wednesday September 19th , 2012)
1
Graded problems
1. A particle slides on the inside surface of
PHY 5246: Theoretical Dynamics, Fall 2012
Assignment # 1, Solutions
Problem 1
y
cos
r
sin
r
r=
sin
cos
r
x
Starting from the position vector for a planar motion in polar coordinates
r = r ,
r
we
PHY 5246: Theoretical Dynamics, Fall 2012
September 5th , 2012
Assignment # 2
(Graded problems are due Wednesday September 12th , 2012)
1
Graded problems
1. A bead of mass m slides without friction in
PHY 5246: Theoretical Dynamics, Fall 2012
August 29th , 2012
Assignment # 1
(Due Wednesday September 5th , 2012)
1. Consider a planar motion. In Cartesian coordinates a general vector takes the form,