Computer Controlled Seesaw
1998 SKADRON PRIZE IN
COMPUTATIONAL
PHYSICS
Develop a subroutine that controls the motion of
two
identical balls that slide under the influence of gravity on a 2 meter
long
frictionless seesaw beam pivoting about the center of the beam. The
balls
are allowed to slide for a time interval DT during which the seesaw
has a
constant slope angle a. After each time interval your subroutine
should
return a new value of the slope angle a to be used to continue the
evolution
of the balls for the next time interval. At the ends of the
seesaw there
are perfectly reflecting boundaries. In case the two balls
collide, they
will perfectly reflect off each other. The goal is to
predict an angle
a such that the "distance" from each ball to the
center of the
seesaw, x12+x22, is as small as
possible after each interval. The precise
value for the duration of each
time interval DT will be a random number
uniformly distributed between 0
and 100 milliseconds.
The challenge: Write
a Fortran subroutine CHOICE(X1,V1,X2,V2,SLOPE_ANGLE),
which uses the present
location and velocity for ball-1 (X1, V1) and ball-2
(X2, V2) as input parameters
to compute a new slope angle SLOPE_ANGLE as
output. This angle will be
used for the evolution of the balls during the
next interval from their
position and velocities at the end of the previous
interval. The initial
condition for the first interval for the balls is x1
= -0.5 m, v1= 0.2 m/s,
x2 = 0.3 m, v2 = -0.1 m/s. The slope angles must be
in the interval -45<a<45.
Use g = 10 m/s2 for the
acceleration due to gravity.
The
Prize committee will load your control subroutine
CHOICE into its master
code which simulates the motion of the two balls.
Your subroutine has to
provide the values of the slope angles for 10000
time intervals. The
distance x12+x22 will be computed after each time
interval
and the winning subroutine minimizes this quantity averaged over
all 10000
intervals.
Prize money: $300
($ 200
for the winning team, $100 for the second best
team).
Eligibility: Any
Physics majors in the Department of Physics at
ISU.
Deadline:
4
pm, January 18, 1998. The
winner will be announced at the first
departmental colloquium of the Spring 1999 semester..
Questions: A
copy of the Fortran code that
simulates the motion of the balls for a given slope
angle can be obtained
from any member of the Skadron Prize committee: Drs.
R. Grobe, R.F. Martin,
and Q. Su.
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