TRANSITION TO CHAOS IN THE DAMPED & FORCED NON-LINEAR OSCILLATOR
نویسندگان
چکیده
منابع مشابه
Linear Fractionally Damped Oscillator
The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...
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In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.
متن کاملMultiple transitions to chaos in a damped parametrically forced pendulum.
We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying ω0 (the natural frequency of the pendulum) and A (the amplitude of the external driving force). As A is increased, the SP will restabilize after its instability, destabilize again, and so ad infinitum for any given ω0. Its destabilizations (restabilizations) ...
متن کاملTransition to spatiotemporal chaos in the damped Kuramoto-Sivashinsky equation
K. R. Elder, J. D. Gunton, and Nigel Goldenfeld Department of Physics, Oakland University, Rochester, Michigan 48309-4401 Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 Department of Physics, Lehigh University, 16 Memorial Drive East, Bethlehem, Pennsylvania 18015-3182 ~Received 23 May 1996...
متن کاملThe Forced Damped Pendulum : Chaos , Complication and Control
This paper will show that a “simple” differential equation modeling a garden-variety damped forced pendulum can exhibit extraordinarily complicated and unstable behavior. While instability and control might at first glance appear contradictory, we can use the pendulum’s instability to control it. Such results are vital in robotics: the forced pendulum is a basic subsystem of any robot. Most of ...
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ژورنال
عنوان ژورنال: Revista de Investigación de Física
سال: 2009
ISSN: 1728-2977,1605-7724
DOI: 10.15381/rif.v12i01.8722