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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 double pendulum. The benefits of generalized coordinates become apparent with the analysis of a double pendulum. For the two masses m i (i = 1, 2), let r i = (x i, y i), i = 1, 2 define their two trajectories. These vectors satisfy the two constraint equations,
A simple gravity pendulum [1] is an idealized mathematical model of a real pendulum. [2] [3] [4] It is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. Since in the model there is no frictional energy loss, when given an initial displacement it swings back and forth with a constant amplitude. The model ...
"Simple gravity pendulum" model assumes no friction or air resistance. A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. [1] When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position.
English: Six slow-motion videos of the same double pendulum (built with Lego), recorded with a high-speed camera. For each recording, the double pendulum was excited in the same manner. The videos are temporally aligned to show that the behaviour is similar in the beginning and considerably different later – which is due to the butterfly effect.
The equation describes the motion of a damped oscillator with a more complex potential than in simple harmonic motion (which corresponds to the case = =); in physical terms, it models, for example, an elastic pendulum whose spring's stiffness does not exactly obey Hooke's law.
Moreover, a double pendulum may exert motion without the restriction of only a two-dimensional (usually vertical) plane. In other words, the complex pendulum can move to anywhere within the sphere, which has the radius of the total length of the two pendulums. However, for a small angle, the double pendulum can act similarly to the simple ...
A double inverted pendulum is the combination of the inverted pendulum and the double pendulum. The double inverted pendulum is unstable, meaning that it will fall down unless it is controlled in some way. The two main methods of controlling a double inverted pendulum are moving the base, as with the inverted pendulum, or by applying a torque ...