Physics 409: Classical Mechanics
Fall ‘10
5 October 2010
Lecture schedule
:
5 October: finish Ch. 3 (LRL vector, 2body scattering)
7 October: Ch. 4 (rigid body kinematics, orthogonal transformations)
12 October: Ch. 4 Sec. 4.6, 4.7, 4.8, 4.9 (Skip Sec. 4.5)
Reading tips for 7 October
: How many degrees of freedom does a rigid body have? What are
appropriate generalized coordinates? What is the difference between a space fixed coordinate
frame and a body fixed frame? What is an orthogonal matrix?
What are orthogonal
transformations? What are they used for? What are Euler angles?
Reading tips for October 12
: What is Euler’s Theorem for the motion of a body with one point
fixed? What does the rate of change of a vector formula allow you to do? What is the
instantaneous angular velocity vector?
Homework Set #7:
Due Tuesday, 12 October
(1)(a)
Two particles move in a central force field given by the potential
V
(
r
):
where
k
and
a
are positive constants. Find an expression for the
()
64
//
V(r)
k
a r
a r
⎡⎤
=−
⎣⎦
radius
r
c
of a circular orbit. Show that circular orbits are possible only when the condition
c
#
2/3
is satisfied, where
c
is the dimensionless constant,
. Here,
l
is the constant
22
/(
)
cl
k
a
μ
=
angular momentum, and
μ
is the reduced mass of the twobody system.
You should obtain an
analytical result for the dimensionless radius
x
c
=
r
c
/
a
that depends only on the value of
c
and
pure numbers. (One form of the result is a quadratic equation for the variable
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 Fall '10
 Wilemski
 mechanics, Angular Momentum, circular orbit, Celestial mechanics, stable circular orbit, dimensionless radius xc

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