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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]
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.
1_DOF_Pendulum_with_spring-damper_Adams_simulation.ogv (Ogg Theora video file, length 10 s, 786 × 500 pixels, 1.2 Mbps, file size: 1.45 MB) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
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 ...
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.
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.
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
Havok Script (discontinued) ... (Chaos Physics) at an engine level, while Havok Navigation is a stand alone plugin, and Havok Cloth is a separate tool that works ...