Quaternion

In case you remember or use complex ("imaginary") numbers, then quaternions are just a generalisation of complex numbers into 3 dimensions. They are enormously useful for attitude dynamics and anything which flies because they form a continuous representation without singularities. They were properly described by Hamilton in the 1840s, but have links with earlier work by Euler. A few decades later, people began to realise that vector analysis was much easier to think about and visualise, despite being less powerful. Vectors mostly won, and today quaternions are mostly used in spacecraft control, computer graphics, robotics, and signal processing.


There is no point trying to explain how quaternions work here. If you care, start with wikipedia, then build you own quaternion calculator in any language/system/tool you want. If you want to know why they are useful, then the principal argument is gimbal lock - (see previous entry about gimbals) - the loss of one degree of freedom in gimbal control.