Pendulum and double pendulum

Pendulum

A mass is fixed to another mass with a movable joint.

Pendulum with mass, length, time

The most important thing with pendula is its frequency. If you are in resonance, you rock it up, if you are out of resonance, you dampen it down.

If you are swinging a device, then you have to do with this phenomenon.

Double pendulum

The mathematical formulars for the pendulum are easy. The double pendulum makes a big difference. Here it is not easy anymore. For mathematicians the double pendulum is the symbol for chaos and unpredictability.

Double pendulum.

If one cannot calculate the double pendulum in detail, one may tell general properties. This makes a base for considering the properties of a multi pendulum like a sceleton.

When throwing an axe, you want maximum flight with minimum muscle force. And this without hurting the wrist. For that you have to tune your own movement in resonance with that of the axe.

The frequency of the axe beat time. With knives, you may neglect the time beat of the device without damage, but with axes, it is important, because of its mass. You can damage your wrist by handling an axe the wrong way.

Accelarated double pendula
Accelerated double pendula

For non-physicists. Keep in mind the difference between speed and acceleration. Acceleration is the increment or decrement of speed. Taking away acceleration does not mean, that the speed slows down! The speed gets only less, if the acceleration is smaller than zero.