# Double pendulum - Chaotic motion

A normal pendulum has 1 degree of freedom. That is, the motion of that object can be represented by just **1 variable (ϴ).
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**Here the joint will help the arm of the pendulum to move to and fro.**

The time for one complete cycle, an upswing and a downswing, is called the **period. **The period depends on the **length (L)** of the pendulum.

The **Time period **of the pendulum is given by,

Where **g** is the acceleration due to gravity and **L** is the length of the pendulum.**Below is a table showing the values of time and angle and the graph shows the relation between both.
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**Double pendulum
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A **double pendulum** is a pendulum with another movable arm attached to its end. The motion of a double pendulum is governed by a set of coupled ordinary differential equations. But at certain points the motion is **chaotic**.

A chaotic motion is a type of motion that cannot be predicted mathematically by any means. It produces a different set of results or path of motion each time the motion occurs

Here we can see the two joints that make both the arms to move freely. The motion of Double pendulum is pretty complex and it can be described by a set of differential equations, which is given below

Where ϴ_{1 }and ϴ_{2 }are the angles at joint 1 and joint 2.

**Below is a simulation of the chaotic motion of double pendulum**

*The motion of a Double pendulum is shown in the animation below*