Chaos - Two Double Physical Pendula

Purpose

To illustrate the modern concept of chaos.◙

Equipment

Double physical pendula on base with lead bricks.

Suggestions

Keep hands away after starting.◙

Images

g1-60

Description

The two pendula are started into apparently identical oscillations, but their motion soon diverges. No matter how closely the motions of the two pendula are started, they eventually must undergo virtually total divergence. This illustrates the modern meaning of "chaos."◙

References

W. Stadler, Am. J. Phys 50, 595-598 (1982). ◙Stephen F. Felszeghy, On the adequacy of Newtonian particle mechanics for solving the rigid double pendulum problem, AJP◙53, 230-232 (1985). ◙W. Stadler, Rebuttal to "On the adequacy of Newtonian particle mechanics for solving the rigid double pendulum problem,"◙[AJP 53, 230-232 (1985)], AJP 53, 233-234 (1985). ◙Shinbrot, Grebogi, Wisdom, and Yorke, Chaos in a Double Pendulum, AJP 60, 491-499, (1992). ◙Supplemental Information Sheet, T. Shinbrot, (1989). ◙R. B. Levien and S. M. Tan, Double pendulum: An experiment in chaos, AJP 61, 1038-1044 (1993).