Comments on a new parameterization of the attitude kinematics

Recently, a new formulation has been introduced for the description of attitude kinematics, which is based on two perpendicular rotations. The new parameterization bridges the gap between the Eulerangle (three rotations) and Euler-Rodrigues (one rotation) parameterizations and sheds new light on attitude kinematics. In this paper we present a slightly different derivation (again based on stereographic projection of a column of the rotation matrix) with a different choice of variables. We show the relation of the new parameterization to established formulations and cite examples in which the new description presents special advantages in deriving analytic solutions and in designing control laws.

[1]  T. Kane.  Solution of Kinematical Differential Equations for a Rigid Body , 1973 .

[2]  Panagiotis Tsiotras,et al.  A novel approach to the attitude control of axisymmetric spacecraft , 1995, Autom..

[3]  P. Tsiotras,et al.  New kinematic relations for the large angle problem in rigid body attitude dynamics , 1994 .

[4]  J. V. D. Ha,et al.  Perturbation solution of attitude motion under body-fixed torques , 1985 .

[5]  J. N. Blanton,et al.  A nonlinear oscillator analog of rigid body dynamics , 1973 .

[6]  John L. Junkins,et al.  Perturbation formulations for satellite attitude dynamics , 1976 .

[7]  James M. Longuski,et al.  A New Parameterization of the Attitude Kinematics , 1995 .

[8]  E. Leimanis.  The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point , 1965 .

[9]  James M. Longuski.  Solution of Euler's Equations of Motion and Eulerian Angles for near symmetric rigid bodies subject to constant moments , 1980 .

[10]  U. T. Bödewadt.  Der symmetrische Kreisel bei zeitfester Drehkraft , 1952 .

[11]  G. A. Miller,et al.  MATHEMATISCHE ZEITSCHRIFT. , 1920, Science.

[12]  M. Shuster.  A survey of attitude representation , 1993 .

[13]  An approximate solution of the equations of motion for arbitrary rotating spacecraft , 1966 .

[14]  Panagiotis Tsiotras.  On the optimal regulation of an axi-symmetric rigid body with two controls , 1996 .

[15]  Malcolm D. Shuster.  Survey of attitude representations , 1993 .

[16]  DynamicsJames M. Longuski,et al.  Analytic Solution of the Large Angle Problem in Rigid Body Attitude Dynamics , 1995 .

[17]  Panagiotis Tsiotras,et al.  Spin-axis stabilization of symmetric spacecraft with two control torques , 1994 .

[18]  James M. Longuski.  Real solutions for the attitude motion of a self-excited rigid body , 1991 .

[19]  M. Shuster.  The kinematic equation for the rotation vector , 1993 .

[20]  John E. Cochran,et al.  Attitude Motion of Asymmetric Dual-Spin Spacecraft , 1980 .

[21]  G. Darboux.  Leçons sur la théorie générale des surfaces , 1887 .

[22]  Panagiotis Tsiotras,et al.  A complex analytic solution for the attitude motion of a near-symmetric rigid body under body-fixed torques , 1991 .

[23]  R. S. Armstrong.  Errors Associated with Spinning-up and Thrusting Symmetric Rigid Bodies , 1965 .

[24]  John L. Junkins,et al.  Analytical solutions for Euler parameters , 1974 .