Abstract

Repeat the problem before, but give the two penduluns slightly different damping factors. Compare the lyapunce with that found in figure 3.7

Background

The dips of Δθ occur when one of the penduluns reachs a turnning point. Δθ
will vanish near each turning point since the trajectories away form these dips in Figure 3.7. These platean values of Δθ exhibit a steady and fairly rapid decrease with t.This means that the motion of the two pendulums becomes more and more similar,since the difference decreased by six orders zreo as the motion orceeds.

Main body

The code

Here is the formula. (They were photograghed on the book)

Here is the result when Fd is 0.5 and Fd is9.5

Conclusion

We can see that when Fd is 0.5,the different system would tend to getclose to each other.

And when Fd is 9.5, the differences between each other would be larger and larger.

Reference

Thanks for cuilihao's code