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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]
An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259 [13] 20 examples of periodic solutions to the three-body problem In the 1970s, Michel Hénon and Roger A. Broucke each found a set of solutions that form part of the same family of solutions: the Broucke–Hénon–Hadjidemetriou family.
Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics.
Any swinging rigid body free to rotate about a fixed horizontal axis is called a compound pendulum or physical pendulum. A compound pendulum has the same period as a simple gravity pendulum of length ℓ e q {\displaystyle \ell ^{\mathrm {eq} }} , called the equivalent length or radius of oscillation , equal to the distance from the pivot to a ...
Noteworthy examples include the three-body problem, the double pendulum, dynamical billiards, and the Fermi–Pasta–Ulam–Tsingou problem. Newton's laws can be applied to fluids by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighboring pieces.
A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. 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 towards the equilibrium position.
For a free, rigid beam, an impulse is applied at right angle at a point of impact, defined as a distance from the center of mass (CM). The force results in the change in velocity of the CM, i.e. d v c m {\displaystyle dv_{cm}} :
Motion of Swinging Atwood's Machine for M/m = 4.5. The swinging Atwood's machine is a system with two degrees of freedom. We may derive its equations of motion using either Hamiltonian mechanics or Lagrangian mechanics.