2.032 DYNAMICS
Fall 2004
Problem Set No. 8
Out
: Wednesday, November 10, 2004
Due
: Wednesday, November 17, 2004
at the beginning of class
Problem 1
Reconsider Problem 1 of Quiz No.1.
As shown in the figure, the flywheel spins at a
constant rate
ω
2
, and also rotates about
z
axis with angular velocity
ω
1
that is a function
of time. The center of mass of the flywheel is located on the
z
axis, and the centroidal
moments of inertia are
I
1
about the spin axis and
I
2
transverse to that axis
(a) Derive the Lagrangian equations of motion.
(b) Find the generalized forces necessary to maintain the motion.
1
1
z
Outer
gimbal
Inner gimbal
2
w
q
w
Figure by OCW.
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Problem 2
(from Doctoral Qualifying Exam 2002)
Two identical rigid cylinders, each having radius
R
and mass
m
, are linked by a connecting
rod of length 3
R
and mass
M
as shown below. A horizontal force
F
(
t
) is applied to the
center of the right cylinder and neither cylinder slips in its rolling motion. In the initial
position, the angle
θ
locating the connecting pin is zero. Derive the Lagrangian equations
of motion for this system.
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 Fall '04
 GeorgeHaller
 Angular Momentum, Rotation, Ginsberg, Lagrangian equations

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