# Euclid's Muse

## your source for INTERACTIVE math apps

Create an Account

# Search Results for “chaos”

##### Simple Chaos Machine
Changing the spring constant (k) illustrates the onset of chaos in this simple mechanism.

Tags: chaos, wolfram

##### double pendulum
A double pendulum can yield chaotic motion.

Tags: chaos, mechanical-expressions

##### Double Pendulum
A double pendulum is a simple example of a chaotic machine.

Tags: dynamics, chaos

##### Catastrophe
L is the natural length of the spring AD.  AC is length 4. Set L to be 3.  How many stable positions are there?  (You can drag D to different start points on the line and see where it goes.) Try dragging B to rotate the line.  How does it affect the stable positions? Now change L to 6, but move B so the line is horizontal.  How many stable positions are there? Now move B  so that the line slopes down from D to C.  Observe that D moves slowly towards C until the stable point disappears and it moves "catastrophically" to the other stable point. This example is from Steven H Strogatz Nonlinear Dynamics and Chaos

Tags: catastrophe, dynamics

##### A Chaotic Flywheel
The left hand flywheel is driven at a constant velocity. The right hand wheel is connected by a spring, whose natural length is equal to the distance between the centers of the flywheels, and whose stiffness is k. Output is the angle (in radians) of the flywheel. Note that when k is approximately 5, the motion is regular. Try different values of k, and observe the onset of chaos.

Tags: Mechanical-Expressions, Mechanics, Chaotic, Flywheel, Spring, Simulation