Chaos of the Double Pendulum
نویسنده
چکیده
We characterized the chaotic motion of a damped physical double pendulum which has not been achieved previously. The results consist of scattered phase plots, fractal Poincaré sections, and positive Lyapunov exponents.
منابع مشابه
Chaos in a double pendulum
A novel demonstration of chaos in the double pendulum is discussed. Experiments to evaluate the sensitive dependence on initial conditions of the motion of the double pendulum are described. For typical initial conditions, the proposed experiment exhibits a growth of uncertainties which is exponential with exponent A = 7.5 ± 1.5 s• Numerical simulations performed on an idealized model give good...
متن کاملDynamics of a double pendulum with distributed mass
We investigate a variation of the simple double pendulum in which the two point masses are replaced by square plates. The double square pendulum exhibits richer behavior than the simple double pendulum and provides a convenient demonstration of nonlinear dynamics and chaos. It is also an example of an asymmetric compound double pendulum, which has not been studied in detail. We obtain the equil...
متن کاملExploration of the Double Pendulum
The double pendulum is a classic system in the study of chaos. We have explored the double pendulum experimentally, and compared results to a numerical simulation. This comparison was done in the time it takes for the second arm of the pendulum to ”flip,” based on initial starting conditions. We also performed analyis of the vertically driven case.
متن کاملMelnikov’s Method Applied to the Double Pendulum
Melnikov’s method is applied to the planar double pendulum proving it to be a chaotic system. The parameter space of the double pendulum is discussed, and the integrable cases are identified. In the neighborhood of the integrable case of two uncoupled pendulums Melnikov’s integral is evaluated using residue calculus. In the two limiting cases of one pendulum becoming a rotator or an oscillator,...
متن کاملExperimental control of high-dimensional chaos: The driven double pendulum.
Chaos control techniques exploit the sensitivity of chaos to initial conditions by applying feedback perturbations to an accessible system parameter. Most methods apply only one perturbation per period and are thus susceptible to control failure when applied to highly unstable systems. Here we extend a recently developed model-independent, quasicontinuous chaos control technique to stabilize a ...
متن کامل