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Singularities of general one-dimensional motions of the plane and space

Published online by Cambridge University Press:  14 November 2011

C. G. Gibson  and
C. A. Hobbs
C. G. Gibson
Affiliation:
Department of Mathematics, University of Liverpool, PO Box 147, Liverpool L69 3BX. e-mail: su07@uk.ac.liverpool.ibm, cahobbs@brookes.ac.uk
C. A. Hobbs
Affiliation:
Department of Mathematics, University of Liverpool, PO Box 147, Liverpool L69 3BX. e-mail: su07@uk.ac.liverpool.ibm, cahobbs@brookes.ac.uk
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Extract

Local models are given for the singularities which can appear on the trajectories of general one-dimensional motions of the plane or space. Versal unfoldings of these model singularities give simple pictures describing the family of trajectories arising from small deformations of the tracing point.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 3 , 1995 , pp. 639 - 656
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Bruce, J. W.. Simple singularities of mappings (ℂ,0)→(ℂ2, 0) (preprint, University of Liverpool, 1978).Google Scholar
2Bruce, J. W. and Gaffney, T. J.. Simple singularities of mappings (ℂ,0)→(ℂ2,0). J. London Math. Soc. 26 (1982), 465–74.CrossRefGoogle Scholar
3Bruce, J. W. and du Plessis, A. A.. Complete transversals (in preparation).Google Scholar
4Bruce, J. W., du Plessis, A. A. and Wall, C. T. C.. Determinancy and unipotency. Inventiones Math. 88 (1989), 521–4.CrossRefGoogle Scholar
5Donelan, P. S.. Generic Properties in Euclidean Kinematics (Ph.D. Thesis, University of Southampton, 1984).Google Scholar
6Donelan, P. S.. Generic properties in Euclidean kinematics. Acta Appl. Math. 12 (1988), 265–86.CrossRefGoogle Scholar
7Donelan, P. S.. On the geometry of planar motions (preprint, Victoria University of Wellington, 1991).Google Scholar
8Gibson, C. G. and Hobbs, C. A.. Singularities of general two-dimensional motions in the plane. To appear in New Zealand J. Math. (1995).CrossRefGoogle Scholar
9Gibson, C. G. and Hobbs, C. A.. Simple singularities of space curves. Math. Proc. Cambridge Philos. Soc. 113(2) (1993), 297–310.CrossRefGoogle Scholar
10Gibson, C. G., Hobbs, C. A. and Marar, W. L.. Singularities of general two-dimensional motions of space (in preparation, 1995).CrossRefGoogle Scholar
11Gibson, C. G. and Newstead, P. E.. On the geometry of the planar 4—bar mechanism. Acta Appl. Math. 7 (1986), 113–35.CrossRefGoogle Scholar
12du Plessis, A. A. and Tari, F.. Classification of map-germs (ℝn, 0) → (ℝp, 0), with n + p ≦ 6 (preprint, University of Aarhus, Denmark, 1992).Google Scholar
13David, J. M. M. Soares. Projection-Generic Maps and Applications (M.Sc. Thesis, University of Liverpool, 1981).Google Scholar
14Tari, F., Some Applications of Singularity Theory to the Geometry of Curves and Surfaces (Ph.D. Thesis, University of Liverpool, 1990).Google Scholar
15Wall, C. T. C.. Geometric Properties of Differentiable Manifolds, Geometry and Topology, Rio de Janeiro, Lecture Notes in Mathematics 597, pp. 707–74 (Berlin: Springer, 1976).Google Scholar
16Wall, C. T. C.. Finite determinancy of smooth map-germs. Bull. London Math. Soc. 13 (1981), 481–539.CrossRefGoogle Scholar
17Wilkinson, T.. The Geometry of Folding Maps (Ph.D. Thesis, University of Newcastle, 1991).Google Scholar