Thursday, February 6, 2014 3:30 pm
-
3:30 pm
EST (GMT -05:00)
MC 5158
Speaker
Prof. Dong Eui Chang, Department of Applied Mathematics, University of Waterloo
Title
On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems
Abstract
The
falling
cat
problem
has
been
very
popular
in
control,
mechanics
and
mathematics
since
Kane
and
Sher
published
a
paper
on
this
topic
in
1969.
A
cat,
after
released
upside
down,
executes
a
180-degree
reorientation,
all
the
while
having
a
zero
angular
momentum.
It
makes
use
of
the
conservation
of
angular
momentum
that
is
induced
by
rotational
symmetry
in
the
dynamics.
In
general,
however,
the
angular
momentum
is
not
conserved
if
there
is
a
symmetry-breaking
force,
such
as
a
frictional
force,
on
the
system.
Recently,
we
have
discovered
an
exciting
phenomenon
in
controlled
mechanical
systems
with
external
damping
forces.
If
a
control
force
is
activated
on
such
a
system
for
a
while
and
then
gets
deactivated,
the
unactuated
cyclic
variables,
which
get
excited
initially
from
rest
by
the
control
force,
eventually
all
converge
back
to
their
initial
values
as
time
tends
to
infinity,
which
is
called
a
damping-induced
self-recovery
phenomenon.
A
self-recovery
phenomenon
can
be
observed
in
the
simple
experiment
with
a
rotating
stool
and
a
bicycle
wheel
which
is
a
typical
setup
in
physics
classes
to
demonstrate
the
conservation
of
angular
momentum.
Sitting
on
the
stool,
one
spins
the
wheel
by
hand
while
holding
it
horizontally.
A
reaction
torque
will
be
created
to
initiate
a
rotational
motion
of
the
stool
in
the
opposite
direction.
After
some
time,
if
the
person
applies
a
braking
force
halting
the
wheel
spin,
then
the
stool
will
asymptotically
return
to
its
original
position,
as
if
it
has
a
memory,
provided
that
there
is
a
viscous
damping
force
on
the
rotation
axis
of
the
stool.
We
have
also
discovered
the
self-recovery
phenomenon
in
incompressible
viscous
fluid
flows.
As
a
corollary,
we
give
a
"dynamic"
explanation
of
the
famous
experiment
by
G.I.
Taylor
on
the
"kinematic"
reversibility
of
low-Reynolds-number
flows.
In
this
talk,
several
videos
will
be
displayed
to
show
instances
of
damping-induced
self-recovery
phenomena.