ENERGY-CONSERVATION AND CHAOS IN THE GRAVITATIONALLY DRIVEN FERMI OSCILLATOR

Chaotic dynamics of the two-body conservative system, which consists o f a particle of mass m bouncing elastically on a horizontal plate of m ass M supported by an elastic spring, is investigated. The system inte grates the properties of coupled oscillators with those of the bouncin g-ball and impact oscillator problems. Results obtained by varying the mass ratio Mim and the spring constant k in numerical computations ar e presented in the form of time-dependent diagrams and discrete maps. The rich variety of resulting chaotic behavior includes strange attrac tors with fractal structure, resonant islands, crisis, and intermitten cy route to chaos. The system has a remarkable didactic value as an ex ample of chaotic behavior in simple systems close to everyday experien ce. The integrable limit M=0 is appropriate for introducing the phase portraits and discussing the interrelationship between the shape of th e potential energy curves and the resulting oscillatory motion. (C) 19 98 American Association of Physics Teachers.