Double Pendulum: Chaos Theory

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Research question: To what extent is the maths behind the double pendulum correct and what are its limitations due to chaos theory.

Chaos theory is the idea, in simple terms, that certain natural events and occurrences are unpredictable in their behaviour. Examples of this are: weather, turbulent flow in certain liquids and even the double pendulum. These things can be explored and determined mathematically just how unpredictable they are and under what conditions they may become predictable, looking at the example of the double pendulum.

What is chaos theory?
Chaos theory can be broken down into six different principles: Butterfly effect, unpredictability, order/disorder chaos, fractals, feedback and mixing. Although I will only be looking at the principles related to the double pendulum which are; the butterfly effect, unpredictability, order/ disorder chaos, and mixing. The butterfly effect, is a principle which states that an event as insignificant as a butterfly flapping its wings can change the course of history, such as causing a hurricane on the other side of the globe. Earth is a big system, but it can be affected by everything and anything in that system, such as a nuclear bomb being dropped or a butterfly flapping its wings. The unpredictability …show more content…
The meaning of limitations in this context is that there is a certain angle at which it is possible to predict what is going to happen using mathematics and after that certain point there are too many variables to be able to realistically know what the behaviour of the oscillations will be. Under the same conditions with the same equipment but two different times the double pendulum will not produce the same chaotic pattern. This then causes an issue when trying to represent the motion mathematically if there is no visible pattern, because mathematics looks at quantifying

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