  The parameterisation of rotations in three dimensional Euclidean space is an
area of applied mathematics that has long been studied, dating back to the
original works of Euler in the 18th century. As such, many ways of
parameterising a rotation have been developed over the years. Motivated by the
task of representing the orientation of a balancing body, the fused angles
parameterisation is developed and introduced in this paper. This novel
representation is carefully defined both mathematically and geometrically, and
thoroughly investigated in terms of the properties it possesses, and how it
relates to other existing representations. A second intermediate
representation, tilt angles, is also introduced as a natural consequence
thereof.
