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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]
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 ...
The system indeed appears to exhibit a great dependence on initial conditions, a defining property of chaotic systems; moreover, two attractors of the system are seen in both plots. The Malkus waterwheel, also referred to as the Lorenz waterwheel or chaotic waterwheel, [1] is a mechanical model that exhibits chaotic dynamics.
The Duffing equation is an example of a dynamical system that exhibits chaotic behavior. Moreover, the Duffing system presents in the frequency response the jump resonance phenomenon that is a sort of frequency hysteresis behaviour.
In order to make a prediction about the system's future behavior, an analytical solution of such equations or their integration over time through computer simulation is realized. The study of dynamical systems is the focus of dynamical systems theory , which has applications to a wide variety of fields such as mathematics, physics, [ 4 ] [ 5 ...
When three bodies orbit each other, the resulting dynamical system is chaotic for most initial conditions. Because there are no solvable equations for most three-body systems, the only way to predict the motions of the bodies is to estimate them using numerical methods. The three-body problem is a special case of the n-body problem.
A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear systems (especially partial differential equations).They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems.
Similarly, the state space of the N=3 case is a 2-dimensional torus, and so the system evolves as a flow on the 2-torus, which cannot be chaotic. Chaos first occurs when N=4. For some settings of ω 1 , ω 2 , ω 3 , K {\displaystyle \omega _{1},\omega _{2},\omega _{3},K} , the system has a strange attractor .