Double pendulum
This activity belongs to the GeoGebra book The Domain of the Time.
If we place a pendulum at the moving end of another, we obtain a double pendulum. Although each of them continues to be governed by the stable period of an ordered motion, their combined movement results in chaos.
We can take advantage of the polyline generated by the trace to estimate the distance traveled by the second pendulum.
SCRIPT FOR SLIDER anima
# Calculate the elapsed seconds dt; add one second if t1(1) < tt
SetValue(tt, t1(1))
SetValue(t1, First(GetTime(), 3))
SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)
# Move M1 and M2
SetValue(v1, vt1 + dt gt1)
SetValue(v2, vt2 + dt gt2)
SetValue(M1, M1 + dt v1)
SetValue(M2, M2 + dt v2)
# Add the position M2 to the record for the polyline trace
SetValue(reg, Append(reg, M2))
Author of the activity and GeoGebra construction: Rafael Losada.