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Chaos & Nonlinear Dynamics

  • G1-60 CHAOS - TWO BIFILAR PENDULA

    G1-60
    Illustrates chaotic motion
    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.

    Eric Neumann has created an online simulation that can be used to model one of the legs of the pendulum. Try experimenting with the simulation as well, and see how sensitive it can be to its initial conditions. https://www.myphysicslab.com/pendulum/double-pendulum-en.html

    G1

  • G2-08: DRIVEN NONLINEAR OSCILLATOR

    G2-08
    Demonstrate amplitude "jumps" and resonance hysteresis in Duffing's equation.
    The clamped hacksaw blade with a magnet and mirror attached to its free end is a non-linear oscillator. A laser reflected off the mirror is used as an indicator of the motion. Driving the oscillator with a Wavetek sine generator using a small coil one can observe: (1) sudden changes in amplitude as the frequency is very slowly changed, and (2) hysteresis in the oscillation amplitude at a given frequency, which depends on whether the frequency is being increased or decreased. The frequency can be most readily measured with a digital meter measuring the period of the driving sine wave.

  • L3-42: CHAOS - FOUR REFLECTING SPHERES

    L3-42
    Demonstrate the mathematical concept of chaos using the complex multiple reflections off four spheres.
    Four large shiny spheres - the type used as English garden gazing spheres - are placed together as shown in the photograph at the left above. Complex multiple reflections illustrate the behavior of fractals, as seen in the close-up photograph at the right. This apparatus may be in residence in a departmental showcase, in which case a smaller version will be delivered, one using Christmas balls.

    l3-42a