# How the Swinging Sticks Works

The Swinging Sticks sculpture is a deceptively simple construct that inspires wonder into the mechanics of its design. The sculpture is crafted by expert artisans who calibrate the magnets in the arms to allow precise motion. This is to ensure perfection, and is reflected in the 0.01% defect rate over the last 11 years by the manufacturer. Learn more about the Swinging Sticks here.

While it looks easy to make, in fact an advanced knowledge of science, mathematics, and physics is essential to understanding how it is made and works. So where did the idea for the Swinging Sticks come from? Well the concept for the sculpture can be traced back to the idea of perpetual motion, a theory given by many scientific and philosophical minds over the centuries.

## Perpetual Motion Devices

One of the earliest inventors to begin experimenting with perpetual motion was Leonardo Da Vinci who studied the concept in depth and tried to build many different models. Eventually, Da Vinci concluded that perpetual motion impossible and gave up on the idea.

Despite Da Vinci giving up on perpetual motion, many physicists and engineers today are still attempting to design a perpetual motion device. If it was proven to be real we would see things like endless motors requiring no energy because there would be no influence of friction. However, in the world we live in, friction is a very real concept and it thus prevents anything from achieving true perpetual motion based on our modern understanding of physics.

Read More## Physics

The Swinging Sticks sculpture works by mimicking a perpetual motion device through electrical currents and electromagnetic fields. Current physics state that real perpetual motion devices are impossible by modern technology. However, one of the key principles in physics also states that moving electrons generates a magnetic field. This generated magnetic field is what powers the entire sculpture.

The Swinging Sticks contains three coils that serve various functions. Two of the electrical coils are involved with measuring the speed of the rotating sticks. The middle electrical coil is used to adjust the speed either faster or slower depending on the speed judged by the first and last coils.

Built into the arms of the Swinging Sticks are powerful neodym magnets. When these magnets pass through the magnetic field generated by the electrical coils, they are repulsed and get a "boost" of kinetic energy while shooting upwards before effortlessly spinning back down. This process repeats over and over as long as a magnetic field is generated.

The position of the magnets must be extremely precise as not to waste motion or power. Conservation of energy is extremely important in the sculpture in order to provide longevity of battery life.

The authentic Swinging Sticks contains state-of-the-art SFK bearings and special electrical components to reduce the amount of energy consumed.

This is why this sculpture requires 4 AA batteries, not to run a motor, because the sculpture is noiseless in its rotation but to provide an electric current. As long as there are batteries, this sculpture will run forever, endlessly spinning in a generated electromagnetic field. The real Swinging Sticks is manufactured to run for a significant period of time (2+ years) without requiring a change of batteries due to the quality of parts in the sculpture.

## Mathematics

The Swinging Sticks are governed by a series of calculus equations in physics related to double pendulums. This requires understanding differential equations, an extremely advanced area of mathematics. A double pendulum is a pendulum that has another one attached to the end of it. The Swinging Sticks is considered a simple or compound double pendulum because it operates solely in a 2D plain.

For the most part, the motion is seemingly chaotic however there is actually mathematic beauty behind the Swinging Sticks. The Swinging Sticks equations for double pendulums are solved using the Runge-Kutta methods of numerical analysis. This technique was developed in the early 1900's by mathematicians C. Runge and M.W. Kutta

### Model

### Variables

- x = Horizontal Coordinate
- y = Vertical Coordinate
- θ = Angle of Pendulum
- L = Length
- m = mass
- g = gravity (9.81 m/s
^{2})

### Equations

Calculate all the following equations for

x_{1}, x_{2}, y_{1}, y_{2}

1) Calculate the position of masses

x = L sin θ

2) Next take the derivative to find the velocity

x_{1}^{'} = θ_{1}^{'} L_{1} cos θ_{1}

x_{2}^{'} = x_{1}^{'} + θ_{2}^{'} L_{2} cos θ_{2}

3) Take another derivative to find the acceleration

x_{1}^{''} = −θ_{1}^{'2} L_{1} sin θ_{1} + θ_{1}^{''} L_{1} cos θ_{1}

x_{2}^{''} = x_{1}^{''} − θ_{2}^{'2} L_{2} sin θ_{2} + θ_{2}^{''} L_{2} cos θ_{2}

0 = vertical downwards

Counter-clockwise = positive