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The animations below depict the motion of a simple (frictionless) pendulum with increasing amounts of initial displacement of the bob, or equivalently increasing initial velocity. The small graph above each pendulum is the corresponding phase plane diagram; the horizontal axis is displacement and the vertical axis is velocity. With a large ...
"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.
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Simple pendulum, see picture (right). Simple harmonic oscillator where the phase portrait is made up of ellipses centred at the origin, which is a fixed point. Damped harmonic motion, see animation (right). Van der Pol oscillator see picture (bottom right).
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]
English: Phase portrait of an undamped simple pendulum. The latest revision of the image was created in python using the source code provided below. The first revision of the image was plotted using with GNU Octave using gnuplot backend and saved as a standalone LaTeX file. The PDF generated was then converted to SVG using pdf2svg.
English: Diagram of simple gravity pendulum, an ideal model of a pendulum. It consists of a massive bob suspended by a weightless rod from a frictionless pivot, without air friction. When given an initial impulse, it oscillates at constant amplitude, forever
The azimuth , being absent from the Lagrangian, is a cyclic coordinate, which implies that its conjugate momentum is a constant of motion. The conical pendulum refers to the special solutions where θ ˙ = 0 {\displaystyle {\dot {\theta }}=0} and ϕ ˙ {\displaystyle {\dot {\phi }}} is a constant not depending on time.