The evolution of space curves by curvature and torsion
The evolution of space curves by curvature and torsion
We apply Lie group based similarity methods to the study of a new, and widely relevant, class of objects, namely motions of a space curve. In particular, we consider the motion of a curve evolving with a curvature kappa and torsion tau dependent velocity law. We systematically derive the Lie point symmetries of all such laws of motion and use these to catalogue all their possible similarity reductions. This calculation reveals special classes of law with high degrees of symmetry (and a correspondingly large number of similarity reductions). Of particular note is one class which is invariant under general linear transformations in space. This has potential applications in pattern and signal recognition.
9857-9879
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
King, John
7d4e166d-4b3c-4440-a472-ef597d7a01f6
7 November 2002
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
King, John
7d4e166d-4b3c-4440-a472-ef597d7a01f6
Richardson, Giles and King, John
(2002)
The evolution of space curves by curvature and torsion.
Journal of Physics A: Mathematical and General, 35, .
(doi:10.1088/0305-4470/35/46/310).
Abstract
We apply Lie group based similarity methods to the study of a new, and widely relevant, class of objects, namely motions of a space curve. In particular, we consider the motion of a curve evolving with a curvature kappa and torsion tau dependent velocity law. We systematically derive the Lie point symmetries of all such laws of motion and use these to catalogue all their possible similarity reductions. This calculation reveals special classes of law with high degrees of symmetry (and a correspondingly large number of similarity reductions). Of particular note is one class which is invariant under general linear transformations in space. This has potential applications in pattern and signal recognition.
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Journal of Physics A Mathematical and General 2002 Richardson.pdf
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Published date: 7 November 2002
Organisations:
Applied Mathematics
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Local EPrints ID: 404020
URI: http://eprints.soton.ac.uk/id/eprint/404020
ISSN: 0305-4470
PURE UUID: 65e96649-1234-4135-931a-cc48cbb4bfd8
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Date deposited: 19 Dec 2016 16:49
Last modified: 16 Mar 2024 04:00
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John King
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