The dynamics of the Malkus water wheel

POSTER

Abstract

The Malkus water wheel is a mechanical system whose chaotic dynamics are described by the famous Lorenz equations. In our experiment, a continuous series of syringes are attached to a bicycle wheel that can be inclined. Water pours into the wheel at the wheel's top and tunable friction is introduced through magnetic inductance braking. We successfully generate fixed point, periodic, and chaotic motion by tuning the wheel parameters, such as the braking torque, the inflow rate, and the angle of inclination. Upon mapping the experimentally measured parameters onto those of the model, we find that the wheel's behavior agrees reasonably well with that of the Lorenz equation.

Authors

  • Alison Saunders

    Reed College

  • A.N. Behkami

    Kent State University, Reed College, Western Washington University, Washington State University, Department of Physics, University of Idaho, Department of Physics, Whitman College, SciPrint.org, STScI, Physics Dept., Montana State University, Bozeman, MT 59717, Chemistry Dept., Montana State University, Bozeman, MT 59717, Physics Dept., Montana State University, Bozeman, MT 59717; Institut fuer Physik, Technical University Ilmenau, 98693 Ilmenau, Germany, Centre College, Islamic Azad University, Department of Physics, Fars Science and Research Center

  • Lucas Illing

    Reed College