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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Conformal rotation vector | 1/1 | https://en.wikipedia.org/wiki/Conformal_rotation_vector | reference | science, encyclopedia | 2026-05-05T12:04:37.269471+00:00 | kb-cron |
The conformal rotation vector, whose coordinates are also known as modified Rodrigues parameters or Wiener–Milenkovic parameters, is a three-dimensional vector representing a three-dimensional rotation or orientation. It is the stereographic projection of a versor (unit quaternion) onto the pure-imaginary hyperplane. It was first described by Thomas Wiener (1962), called the conformal rotation vector by Veljko Milenkovic (1982), and named the modified Rodrigues vector by Malcolm Shuster (1993). It is related to the Rodrigues vector first described by Olinde Rodrigues (1840) and called by Josiah Gibbs (1884) the vector semitangent of version, whose coordinates are called Rodrigues parameters or Euler–Rodrigues parameters.
== Notes ==
== References == Milenkovic, Veljko (1982), "Coordinates Suitable for Angular Motion Synthesis in Robots", Robots VI: Conference Proceedings, Robots VI, Detroit, Michigan, 2–4 March 1982, Society of Manufacturing Engineers, pp. 407–420 Shuster, Malcolm D. (1993), "A Survey of Attitude Representations" (PDF), The Journal of the Astronautical Sciences, 41 (4): 439–517 Wiener, Thomas Freud (1962), Theoretical Analysis of Gimballess Inertial Reference Equipment Using Delta-Modulated Instruments (Ph.D. thesis), Massachusetts Institute of Technology, hdl:1721.1/14454
== Further reading == Bauchau, Olivier A.; Trainelli, Lorenzo (2003), "The Vectorial Parameterization of Rotation" (PDF), Nonlinear Dynamics, 32: 71–92, doi:10.1023/A:1024265401576 Bruccoleri, Christian; Mortari, Daniele (2006), "MRAD: Modified Rodrigues Vector Attitude Determination", The Journal of the Astronautical Sciences, 54 (3): 383–390, doi:10.1007/BF03256496 Chung, Soon-Jo; Ahsun, Umair; Slotine, Jean-Jacques E. (2009), "Application of synchronization to formation flying spacecraft: Lagrangian approach", Journal of Guidance, Control, and Dynamics, 32 (2): 512–526, doi:10.2514/1.37261 Crassidis, John L.; Markley, Francis Landis (1996), "Attitude estimation using modified Rodrigues parameters", Flight Mechanics/Estimation Theory Symposium, Greenbelt, Maryland, May 14–16, 1996 Hurtado, John E. (2009), "Interior Parameters, Exterior Parameters, and a Cayley-Like Transform" (PDF), Journal of Guidance, Control, and Dynamics, 32 (2): 653–657, doi:10.2514/1.39624 Karlgaard, Christopher D.; Schaub, Hanspeter (2010), "Nonsingular attitude filtering using modified Rodrigues parameters" (PDF), The Journal of the Astronautical Sciences, 57 (4): 777–791, doi:10.1007/BF03321529 Marandi, S.R.; Modi, Vinod J. (1987), "A Preferred Coordinate System and the Associated Orientation Representation in Attitude Dynamics", Acta Astronautica, 15 (11): 833–843, doi:10.1016/0094-5765(87)90038-5 Markley, Francis Landis; Crassidis, John L. (2014), Fundamentals of Spacecraft Attitude Determination and Control, Springer, doi:10.1007/978-1-4939-0802-8 Schaub, Hanspeter; Junkins, John L. (1996), "Stereographic Orientation Parameters for Attitude Dynamics: A Generalization of the Rodrigues Parameters" (PDF), Journal of the Astronautical Sciences, 44 (1): 1–19 Shoham, M.; Jen, F.-H. (1993), "On rotations and translations with application to robot manipulators", Advanced Robotics, 8 (2): 203–229, doi:10.1163/156855394x00464 Terzakis, George; Lourakis, Manolis; Ait-Boudaoud, Djamel (2018), "Modified Rodrigues Parameters: An Efficient Representation of Orientation in 3D Vision and Graphics" (PDF), Journal of Mathematical Imaging and Vision, 60 (3): 422–442, doi:10.1007/s10851-017-0765-x Tsiotras, Panagiotis; Longuski, James M. (1995), "A New Parameterization of the Attitude Kinematics" (PDF), Journal of the Astronautical Sciences, 43 (3): 243–262