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A double pendulum is deterministic but chaotic system — fully governed by Newton’s laws, yet extremely sensitive to initial conditions.

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Physics In History

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56,908 görüntüleme • 3 ay önce •via X (Twitter)

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Mathematics. Physics. Magnetic Chaotic Pendulum: adding magnetic forces to gravity gives this pendulum chaotic motion (sensitivity to slight differences in initial launch conditions). By Physicsfun, Used with permission.
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Mathematics. Physics. Magnetic Chaotic Pendulum: adding magnetic forces to gravity gives this pendulum chaotic motion (sensitivity to slight differences in initial launch conditions). By Physicsfun, Used with permission.

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Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission
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Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission

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Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission
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The Lorenz system is a model that describes chaotic behavior in atmospheric convection. Its study reveals how small changes in initial conditions can lead to different outcomes.
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The Lorenz system is a model that describes chaotic behavior in atmospheric convection. Its study reveals how small changes in initial conditions can lead to different outcomes.

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A double pendulum demonstrates chaos theory, tracing its unpredictable path The dependence on initial conditions, and sensitivity to variation is one of the fundamental properties of chaos This is commonly referred to as "the butterfly effect,"
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Initial conditions: Pendulum 1: position: (1.26, 3.13), mass: 3.25 Pendulum 2: position: (3.98, 4.02), mass: 3.36
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Initial conditions: Pendulum 1: position: (1.26, 3.13), mass: 3.25 Pendulum 2: position: (3.98, 4.02), mass: 3.36

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There truly is an underlying order in every chaotic system In this scene, we have 2500 identical triple pendulums on a grid with almost the same initial conditions.
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There truly is an underlying order in every chaotic system In this scene, we have 2500 identical triple pendulums on a grid with almost the same initial conditions.

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These are 5000 double pendulums each one with different initial conditions: a monument to chaos. [📹 Santiago Ortiz / moebio]
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These are 5000 double pendulums each one with different initial conditions: a monument to chaos. [📹 Santiago Ortiz / moebio]

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In 1890, Henri Poincaré proved the non-existence of the uniform first integral of the three-body problem and the sensitive dependence to initial conditions of its trajectories. Yet, stable solutions to it do exist and this is one of them.
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In 1890, Henri Poincaré proved the non-existence of the uniform first integral of the three-body problem and the sensitive dependence to initial conditions of its trajectories. Yet, stable solutions to it do exist and this is one of them.

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Chaos and the double pendulum: the configuration space of the double pendulum is a torus (a circle for each angle coordinate) so we can plot the evolution of such a pendulum in two ways: either as a "real pendulum" in physical space, or as a point in configuration space :)
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Chaos and the double pendulum: the configuration space of the double pendulum is a torus (a circle for each angle coordinate) so we can plot the evolution of such a pendulum in two ways: either as a "real pendulum" in physical space, or as a point in configuration space :)

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Feels like Kuhio Aloy broke a few of Newton’s laws with this bomb
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Australia is governed by extremely dangerous people The left lie, spin false narratives, and push propaganda. To our faces. All day, everyday
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Double pendulum. Possible to predict these motions?
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Double pendulum. Possible to predict these motions?

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This cult is extremely dangerous, crosses all limits.😬 A newborn’s immune system is extremely weak, Yet this man is putting tongue in the baby’s mouth, Which can be deadly for the child by transferring harmful bacteria or viruses. Such actions are extremely dangerous.😬😐
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"If A.I. can not figure out new physics, its clearly not equal to humans. Physics is the law, everything else is a recommendation. Anyone can break laws created by man, but I am yet to see anyone break the laws of physics."
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Once again, Russian jets 🇷🇺 are breaking Newton’s laws 😎
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Once again, Russian jets 🇷🇺 are breaking Newton’s laws 😎

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