Active versus Passive Rotations
Publication: Journal of Surveying Engineering
Volume 144, Issue 1
Abstract
Active and passive rotations are used in many applied scientific fields, such as engineering, geodesy, and geophysics, just to name a few. However, a source of confusion could arise when both types of rotations are performed sequentially. The author is not aware of any publication where, in a tutorial manner, the relationship between active and passive rotations is coherently described, untangling in the process some of the most typical misconceptions. This technical note is a modest attempt to remedy this void by clarifying, as much as possible, some essential points that may help the understanding of these two varieties of commonly used rotations and how to properly apply them in some practical situations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author acknowledges the three anonymous reviewers for their thoughtful and helpful suggestions. Thanks are also extended to B. H. W. van Gelder for critically reviewing an earlier version of the manuscript.
References
Euler, L. (1775). “Nova methodus motum corporum rigidorum determinandi. Novi Commentari Academiae Scientiarum Imperialis Petropolitanae,20, 208–238.
Kaula, W. (1966). Theory of satellite geodesy, Blaisdell Publishing, Waltham, MA.
Millot, Y., and Man, P. P. (2012). “Active and passive rotations with Euler angles in NMR.” Concepts Magn. Reson., 40A(5), 215–252.
Mueller, I. I. (1969). Spherical and practical astronomy as applied to geodesy, Frederic Ungar Publishing, New York.
Pars, L. A. (1965). A treatise on analytical dynamics, Wiley, New York.
Smith, D., Roman, D., and Hilla, S. (2017). “Blueprint for 2022, Part 1: Geometric coordinates.” NOAA Technical Rep. NOS NGS 62, National Geodetic Survey, Silver Spring, MD.
Soler, T. (1977). “Global plate tectonics and the secular motion of the pole.” Rep. No. 252, Department of Geodetic Science, Ohio State Univ., Columbus, OH.
Soler, T. (1997). “Arbitrary alterations.” GPS World, 8(2), 12–12.
Soler, T. (1998). “A compendium of transformation formulas useful in GPS work.” J. Geod., 72(7–8), 482–490.
Soler, T., and Han, J.-Y. (2017). “On rotation of frames and physical vectors: An exercise based on plate tectonics theory.” GPS Solutions, 21(2), 345–361.
Soler, T., Han, J.-Y., and Weston, N. D. (2016). “Variance–covariance matrix of transformed GPS positions: Case study for the NAD 83 geodetic datum.” J. Surv. Eng., 04015004-1.
Thomson, W., and Tait, P. G. (1879). Principles of mechanics and dynamics (formerly titled treatise of natural philosophy), Cambridge Univ. Press, Cambridge, U.K.
Information & Authors
Information
Published In
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Apr 21, 2017
Accepted: Sep 19, 2017
Published online: Oct 27, 2017
Published in print: Feb 1, 2018
Discussion open until: Mar 27, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.