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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]
A computer-assisted proof of chaotic behavior (more precisely, of positive topological entropy) in Chua's circuit was published in 1997. [6] A self-excited chaotic attractor , known as " the double scroll " because of its shape in the ( x , y , z ) space, was first observed in a circuit containing a nonlinear element such that f ( x ) was a 3 ...
Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal.
A pendulum can help you find answers to yes or no questions. Here's how to use a pendulum and interpret the swinging. If You’re Indecisive, You Need a Pendulum in Your Mystical Tool Kit
A nonlinear dynamical system exhibits chaotic hysteresis if it simultaneously exhibits chaotic dynamics (chaos theory) and hysteresis.As the latter involves the persistence of a state, such as magnetization, after the causal or exogenous force or factor is removed, it involves multiple equilibria for given sets of control conditions.
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Notice the appearance of a "dotted" zone, a signature of chaotic behavior. Orbits of the standard map for K = 0.6. Orbits of the standard map for K = 0.971635. Orbits of the standard map for K = 1.2. Orbits of the standard map for K = 2.0. The large green region is the main chaotic region of the map. A single orbit of the standard map for K=2.0.
In contrast to single type chaotic solutions, recent studies using Lorenz models [41] [42] have emphasized the importance of considering various types of solutions. For example, coexisting chaotic and non-chaotic may appear within the same model (e.g., the double pendulum system) using the same modeling configurations but different initial ...