Search results
Results from the WOW.Com Content Network
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 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.
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 ...
Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.
This chaotic attractor is known as the double scroll because of its shape in three-dimensional space, which is similar to two saturn-like rings connected by swirling lines. The attractor was first observed in simulations, then realized physically after Leon Chua invented the autonomous chaotic circuit which became known as Chua's circuit. [ 1 ]
A particle moving inside the Bunimovich stadium, a well-known chaotic billiard. See the Software section for making such an animation.. A dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections from a boundary.
In this sense, chaotic behavior with ergodic orbits is a more-or-less generic phenomenon in large tracts of geometry. Ergodicity results have been provided in translation surfaces, hyperbolic groups and systolic geometry. Techniques include the study of ergodic flows, the Hopf decomposition, and the Ambrose–Kakutani–Krengel–Kubo theorem.
Instead one must compute them numerically. These modes can give insight into the symbolic dynamics of chaotic maps like the Hénon map. [7] In the mode provided, the stable manifold of the strange attractor can be clearly seen. An approximate Koopman mode of the Hénon map found with a basis of 50x50 Gaussians evenly spaced over the domain.