1992/01/01 by Miroslav Kolář, Godfrey Gumbs · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #Quantum chaos and dynamical systems #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Physics #Attractor #Moment of inertia #Classical mechanics #Inertia #Lorenz system #Nonlinear system #Partial differential equation #Chaotic #Mathematical analysis #Mechanics #Mathematics #Quantum mechanics
paper · doi:10.1103/physreva.45.626
openalex publication_date 1992/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study the chaos for a set of coupled, nonlinear partial-differential equations that originate from the equation of motion and the Fourier transform of the mass-conservation equation for the Malkus waterwheel. Dissipation for this system is produced by an adjustable brake. The braking force, proportional to the angular velocity of the wheel, is responsible for the appearance of chaos. The variation of the moment of inertia with time is taken into account. In the large-time limit, the moment of inertia of the composite system, consisting of the wheel and water, tends to a constant, and the three controlling equations of the set of coupled limit equations reduce to a special case of the Lorenz equations, in which the Rayleigh number \ensuremathρ (here characterizing the distribution of water inflow along the perimeter of the wheel) can also assume negative values. Chaotic attractors of the higher harmonics of the water density have been investigated. Boundaries between various regimes of the wheel's limit behavior (uniform rotation, periodic reversals of spin, chaotic reversals) in the Lorenz parameter space have been found. The Lorenz parameter space has thus been explored in considerably more detail than by previous authors.