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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]
The suspension of X is denoted by SX [1] or susp(X). [2]: 76 There is a variation of the suspension for pointed space, which is called the reduced suspension and denoted by ΣX. The "usual" suspension SX is sometimes called the unreduced suspension, unbased suspension, or free suspension of X, to distinguish it from ΣX.
In physics and mathematics, in the area of dynamical systems, an elastic pendulum [1] [2] (also called spring pendulum [3] [4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. [2]
The above discussion focuses on a pendulum bob only acted upon by the force of gravity. Suppose a damping force, e.g. air resistance, as well as a sinusoidal driving force acts on the body. This system is a damped, driven oscillator, and is chaotic. Equation (1) can be written as
An automobile with highly stiff suspension can be considered to be a rigid body traveling on a plane (a flat, two-dimensional space). This body has three independent degrees of freedom consisting of two components of translation and one angle of rotation. Skidding or drifting is a good example of an automobile's three independent degrees of ...
A chain hanging from points forms a catenary. The silk on a spider's web forming multiple elastic catenaries.. In physics and geometry, a catenary (US: / ˈ k æ t ən ɛr i / KAT-ən-err-ee, UK: / k ə ˈ t iː n ər i / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
This is a suitable choice of generalized coordinate for the system. Only one coordinate is needed instead of two, because the position of the bead can be parameterized by one number, s, and the constraint equation connects the two coordinates x and y; either one is determined from the other. The constraint force is the reaction force the wire ...
In mathematics, two functions are said to be topologically conjugate if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy, and related-but-distinct § Topological equivalence of flows, are important in the study of iterated functions and more generally dynamical systems, since, if the dynamics of one iterative function can be determined, then that ...