I've been working on a program that simulates the chaotic action of a pendulum with magnets near the 'bob'. I represent the pendulum as a constant length rod at an angle to the vertical. The angle is a vector, with the direction being the axis it is rotated around and the magnitude being the angle it is rotated. I finally got it working but only after forcing one of the components of the angle to be zero- the vertical one. Can anyone explain why this is so? I would've thought that since it is free to rotate around any axis that forcing a component to zero wouldn't be necessary. Having three degrees of freedom is redundant though since only two are needed. What is modelled when using all three components of the angle vector?