Inelastic collapse of a ball bouncing on a randomly vibrating platform.
نویسندگان
چکیده
A theoretical study is undertaken of the dynamics of a ball which is bouncing inelastically on a randomly vibrating platform. Of interest are the distributions of the number of flights nf and the total time tauc until the ball has effectively "collapsed," i.e., coalesced with the platform. In the strictly elastic case both distributions have power law tails characterized by exponents that are universal, i.e., independent of the detail of the platform noise distribution. However, in the inelastic case both distributions have exponential tails: P(nf) approximately exp[-theta1nf] and P(tauc) approximately exp[-theta2tauc]. The decay exponents theta1 and theta2 depend continuously on the coefficient of restitution and are nonuniversal; however, as one approaches the elastic limit, they vanish in a manner which turns out to be universal. An explicit expression for theta1 is provided for a particular case of the platform noise distribution.
منابع مشابه
Two Methods for Determining Impact Time in the Bouncing Ball System
Many physical systems can be modelled relatively simply and accurately by a ball bouncing off a surface; hence, the dynamics of this system have been studied by mathematicians and physicists for several decades. If the surface that the ball is rebounding from is fixed, the problem is simple, and can be analyzed as a damped harmonic oscillator. However, if the surface itself is vibrating, very c...
متن کاملThe Completely Inelastic Ball: Analysis and Experiment
We consider the problem of a perfectly inelastic bouncing ball on a vibrating plate subjected to a superposition based input forcing function. Both, analytical and experimental studies are performed and the results from each are compared. The developed theoretical models also incorporate friction and provide a fair agreement with the actual experimental data. Interesting regions on bifurcations...
متن کاملDynamics of a ball on a vibrating plate
We study both analytically and numerically the problem of a partially inelastic bail on a platform vibrating with frequency
متن کاملA novel Lyapunov-like method for the non-autonomous bouncing ball system
The non-autonomous bouncing ball system consists of a point mass m in a constant gravitational field g, which bounces inelastically on a flat vibrating table. The presented Lyapunov-like method is set up for non-autonomous measure differential inclusions and constructs a decreasing step function W above the oscillating Lyapunov function V . Furthermore, it is proven that the attractivity of the...
متن کاملThe Completely Inelastic Bouncing Ball
The motion of the inelastic bouncing ball is examined. The time of flight is modelled through numerical simulation using MATLAB. Then the time of flight is experimentally verified using a metal block constrained to move in one direction mounted to a vibration table. Time of flight is measured using a continuity sensor. Bifurcation diagrams are created for a range of accelerations and compared t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 76 3 Pt 1 شماره
صفحات -
تاریخ انتشار 2007