Thanks, Jim. I do indeed have this inclination. In fact my original
intent was to use the simple pendulum to learn and apply the Runge-
Kutta Method. I just haven't gotten around to it yet. Might your
suggestion be a variation of this?
Cheers, Roger
On Oct 31, 2005, at 2:32 AM, [EMAIL PROTECTED]
wrote:
If you have the inclination, you might want to tackle the large
amplitude pendulum. There is no nice analytic solution but you could
numerically integrate the equation of motion. Something like this:
Let A represent the angle. Then you would do a numerical
integration with
repeat loop
set the location of the pendulum to R,A --using radial coordinates
add c * sine(A) to the angular velocity -- where c depends on the
mass, L and g
--The angular acceleration is proportional to the torque which is
proportional to sine(A)
--For small amplitudes sine(A) = A, in radial coordinates
add the angular velocity to A
end repeat loop
Where I have assumed the time interval between loops is one second,
so that dt =1
It would be interesting to show how the period (determined by the
number of loops between changes in sign of the angular velocity)
depends on the amplitude. Show that the clock slows down as it runs
down, i.e. the period decreases with decreasing amplitude--albeit
slowly; it is a second order effect in the amplitude. That's why
pendulum clocks work so well.
Jim
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