  The attitude space has been parameterized in various ways for practical
purposes. Different representations gain preferences over others based on their
intuitive understanding, ease of implementation, formulaic simplicity, and
physical as well as mathematical complications involved in using them. This
technical note gives a brief overview and discusses the quaternions, which are
fourth dimensional extended complex numbers and used to represent orientation.
Their relationship to other modes of attitude representation such as Euler
angles and Axis-Angle representation is also explored and conversion from one
representation to another is explained. The conventions, intuitive
understanding and formulas most frequently used and indispensable to any
quaternion application are stated and wherever possible, derived.
