  In this paper, the intuitive idea of tilt is formalised into the rigorous
concept of tilt rotations. This is motivated by the high relevance that pure
tilt rotations have in the analysis of balancing bodies in 3D, and their
applicability to the analysis of certain types of contacts. The notion of a
'tilt rotation' is first precisely defined, before multiple parameterisations
thereof are presented for mathematical analysis. It is demonstrated how such
rotations can be represented in the so-called tilt phase space, which as a
vector space allows for a meaningful definition of commutative addition. The
properties of both tilt rotations and the tilt phase space are also extensively
explored, including in the areas of spherical linear interpolation, rotational
velocities, rotation composition and rotation decomposition.
