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A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]
The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
Chaos theory. Chaos argument; Butterfly effect; 0-1 test for chaos; ... Double pendulum; Foucault pendulum; Spherical pendulum; Kinematics; Equation of motion ...
Plot of the Duffing map showing chaotic behavior, where a = 2.75 and b = 0.15. Phase portrait of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior.
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Celso Grebogi FRSE (born 1947) is a Brazilian theoretical physicist who works in the area of chaos theory. He is one among the pioneers in the nonlinear and complex systems and chaos theory. Currently he works at the University of Aberdeen as the "Sixth Century Chair in Nonlinear and Complex Systems".