ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 6
Due: July 23, 2010
Q1.
Two wheels, each of mass
m
, are connected by a massless axle of length
l
.
Each
wheel is considered to have its mass concentrated as a particle at its hub.
The wheels roll
without slipping on a horizontal plane.
The hub of wheel A is attached by a spring of
stiffness
k
and unstressed length
l
to a fixed point O.
Use
r
,
, and
as generalized
coordinates.
Then, find: (a) the constraints satisfied by these three variables; (b) the
relationships between the virtual displacements in the three variables; (c) if the
constraints are holonomic or nonholonomic.
(see Problem 625 in the text for a
figure).
Q2.
(see Problem 67 in the text for a figure).
A double pendulum consists of two
massless rods of length
l
and two particles of mass
m
which can move in the vertical
plane.
Assume frictionless joints and define the configuration of the system using the
coordinates
and
.
Recall that the system is in the vertical plane.
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 Fall '10
 BAJAJ
 holonomic systems, Generalized coordinates

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