Appendix A: Characterization of Torque-Free Euler Rotational Motion

For a target constrained by Newtonian forces referenced to inertial space, the motion of the target can be decomposed into two components: translation of the target's center of mass, and rotation about the target's center of mass (a more extensive discussion of this motion decomposition and its importance in processing field measurement data is presented in appendix F.) The spherical coordinates θ(t), φ(t) introduced in section 2.2 describe the viewing angle from the target to the radar resulting from the rotational component of the target motion, referenced to a target-fixed coordinate system having origin located at the target's center of rotation (CoR). The objective of this appendix is to develop a parameter-based characterization of the rotational motion component constrained by Euler's equations as viewed in the radar's frame of reference. The characterization is valid as long as changes in the target's angular momentum vector as viewed from the radar-fixed frame of reference are small compared to the effects of the rotational motion, and the motion is torque free. For different observation intervals along the trajectory, the torque-free rotational motion referenced to the target angular momentum vector remains unchanged; however, the radar line of sight (LoS) to the target angular momentum vector defined by the angle K will have changed. In appendix F, the case where K varies along the trajectory of the target is considered in detail (see figure F.5).