ESDU 98024 presents a quaternion representation of the conversion of the attitude and motion characteristics of an aeroplane measured in flight to those relative to the earth. Flight measurements from accelerometers and rate gyros provide aeroplane motion characteristics relative to axes fixed within the airframe. Three accelerometers, one aligned along each of three axes, measure components of the total linear time-varying acceleration and three rate gyros measure components of the aeroplane angular velocities about each of those same axes. A review is given of the Euler angle method of axis and motion parameter conversion, whereby the orientation of a moving axis system fixed in the aeroplane to another fixed in the earth can be defined from three separate rotations about each of three axes. The traditional rotation angles are the Euler angles of yaw, pitch and roll and have a direct physical interpretation. This approach is suitable for all aeroplane motions involving pitch angles not approaching 90 degrees, but as the pitch angle approaches 90 degrees, both the rates of change of roll and yaw approach infinity. The quaternion is a four-parameter system, that can also be used to define the attitude of a body in space relative to earth and is shown to be equivalent to a set of 'alternative Euler' angles transformations. Expressions are developed for the body angular velocities in terms of the quaternion parameters and then in terms of rates of change of the quaternion parameters themselves. Block diagrams illustrate the conversion of an aeroplane motion parameters from body to earth axis for Euler angles and for the quaternion parameters.