We all know that lasers kick ass, but beyond a passing familiarity with Real Genius most people don’t realize how cool physics can be.No really. A great example is two pendula attached end to end. Sounds simple, right? Yet, this simple system yields incredibly complex, chaotic motion. Inspired by this site, I decided to throw together an “accurate” physical simulation of this system.
You can drag the pendulum bobs around, and the little red dots set the initial angular velocity. If you’re a precision-oriented type, you can enter values in the boxes. Then hit go and let ‘er rip!
Technical details behind the curtain…
I have to thank Eric Weisstein for deriving the equations of motion for this system on this ScienceWorld site.
This simulation solves eqs. (14) and (19) on the above ScienceWorld page with a fourth-order Runge-Kutta solver. An adaptive step-size algorithm would increase accuracy, and may be implemented later. Gravity is a constant 9.8 m/s. There is no damping, the pendulum arms are massless, and the connections are frictionless. Values displayed are in SI units, except the angles which are degrees for ease of use.
Any other questions, feel free to ask here or email me.