AE 352: Aerospace Dynamics II, Fall 2008
Homework 8
Due Friday, October 31
Problem 1.
Greenwood 626.
Problem 2.
Let the position of a mass
m
be speciﬁed by (
x,y,z
). The mass is in
a potential ﬁeld given by
V
=
1
2
k
(
x
2
+
y
2
+
z
2
)
The mass is constrained according to
2 ˙
x
+ 3 ˙
y
+ 4 ˙
z
+ 5 = 0
a) Find the Lagrangian equations of motion in the form which includes constraint
forces.
b) Using the previous result, solve for the position of the mass as a function of time.
Problem 3.
Consider a satellite moving in a gravitational ﬁeld with potential Φ.
A pendulum of mass
m
and length
l
is attached to the satellite. Let the position
and velocity of the satellite be known (given) functions of time. Let
O
xyz
denote a
coordinate frame attached to the satellite.
a) Write an expression for the constraint on the mass.
b) Is the system holonomic or nonholonomic? Is the constraint scleronomic or
rheonomic?
c) Denoting the
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 Spring '09
 SRI
 Kinetic Energy, Mass, Potential Energy, Lagrangian equations, Aerospace Dynamics

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