2.032 DYNAMICS
Fall 2004
Problem Set No. 2
Out: Wednesday, September 22, 2004
Due: Wednesday, September 29, 2004 at the beginning of class
Problem 1
Show that for any 3
×
3 skew-symmetric matrix
A
,
there exists a 3-dimensional vector
ω
such that for any three-dimensional vector
x
,
Ax
=
ω
×
x
.
Problem 2
Consider the coupled pendula shown in the figure below.
Both rods are massless, with
point masses
m
attached to their ends.
Both joints shown in the figure are frictionless.
The
external force
F
encloses a fixed angle
γ
with the line of the pendulum shown.
The masses
never collide. The constant of gravity is
g.
Questions:
•
Identify the constraints.
•
Determine the number of degrees of freedom.
•
Find the equations of motion for

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