- About this Journal ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 467520, 21 pages
Rigid Body Trajectories in Different 6D Spaces
1School of Systems Engineering, University of Reading, Reading RG6 6AY, UK
2Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XQ, UK
Received 26 April 2012; Accepted 4 June 2012
Academic Editors: G. Goldin, D. Ida, and J. A. Nieto
Copyright © 2012 Carol Linton et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- D. D. Holm, Geometric Mechanics. Part II: Rotating, Translating and Rolling, Imperial College Press, London, UK, 2008.
- J. E. Marsden and T. S. Ratiu, Mechanics and Symmetry: Reduction Theory, 1998.
- K. R. Etzel and J. M. McCarthy, “A metric for spatial displacements using biquaternions on SO(4),” in Proceedings of the IEEE International Conference on Robotics and Automation, pp. 3185–3190, 1996.
- P. M. Larochelle, A. P. Murray, and J. Angeles, “SVD and PD based projection metrics on SE(n),” in On Advances in Robot Kinematics, pp. 13–22, Kluwer Academic Publsihers, 2004.
- M. Craioveanu, C. Pop, A. Aron, and C. Petrişor, “An optimal control problem on the special Euclidean group ,” in Proceedings of the International Conference of Differential Geometry and Dynamical Systems (DGDS '09), vol. 17, pp. 68–78, 2010.
- B. C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, vol. 222 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2003.
- V. Jurdjevic, Geometric Control Theory, vol. 52 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1997.
- D. D. Holm, Geometric Mechanics. Part I: Dynamics and Symmetry, Imperial College Press, London, 2nd edition, 2011.
- A. M. Bloch, Nonholonomic Mechanics and Control: With the Collaboration of J. Baillieul, P. Crouch, and J. Marsden, vol. 24 of Interdisciplinary Applied Mathematics, Springer, New York, NY, USA, 2003.
- J. M. Selig, Geometric Fundamentals of Robotics, Monographs in Computer Science, Springer, New York, NY, USA, 2nd edition, 2005.