This preview shows pages 1–4. Sign up to view the full content.
MEEN 364
Notes from Session on September 22, 2004
304 Fermier Hall, 6:00~7:00 pm
The following problems will be covered.
1.
The major mistakes in HW2.
2.
Several examples of deriving the governing equation of motion.
3.
“Rolling without slipping”.
4.
Questions?
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document MEEN 364
Notes from Session on September 22, 2004
304 Fermier Hall, 6:00~7:00 pm
1)
Derive the governing differential equations of the following system:
b
2
b
4
2
MEEN 364
Notes from Session on September 22, 2004
304 Fermier Hall, 6:00~7:00 pm
Solution:
There are basically two steps to obtain the set of differential equations that represent a system:
1.
The
Kinematics Stage
.
In this stage, the position, velocity and the acceleration of all the rigid bodies are defined. It can
be seen that there are three rigid bodies. The total number of degrees of freedom of the system is
three. The degrees of freedom of the system are defined as the horizontal displacements of the
three bodies of mass
m
1
,
m
2
, and
m
3
. Let the displacement of the bodies of mass
m
1
,
m
2
, and
m
3
be equal to
x
1
,
x
2
, and
x
3
, respectively. The velocity and acceleration of the body with mass
m
1
is
given by
x
˙
1
and
x
˙˙
1
respectively; for body
m
2
, they are
x
˙
2
and
x
˙˙
2
respectively; and the velocity
and the acceleration of the body with mass
m
3
, they are
x
˙
3
and
x
˙˙
3
, respectively. This completes
the kinematics stage.
2.
The
Kinetics Stage
.
In this stage, the Newton’s second law of motion is used to obtain the final governing differential
equations of motion. That law, either for translational or rotational motion, is applied separately
to each rigid body as if it were free in the space, considering links to other bodies as external
forces, in addition to any other force that could be acting on it. To ease this analysis,
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/18/2010 for the course MEEN 364 taught by Professor Staff during the Spring '08 term at Texas A&M.
 Spring '08
 Staff
 Controls

Click to edit the document details