Polypolar coordination and symmetries

Rakcheeva T.A.
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The polypolar system of coordinates is formed by a family of a parametrized on a radius isofocal of kf-lemniscates. As well as the classical polar system of coordinates, it characterizes a point of a plane by a polypolar radius ρ and polypolar angle φ. For anyone connectedness a family isometric of curve ρ = const – lemniscates and family gradient of curves φ = const – are mutually orthogonal conjugate coordinate families. The singularities of polypolar coordination, its symmetry, and also curvilinear symmetries on multifocal lemniscates are considered.

Keywords: curves, focuses, multifocal lemniscates, Cassini ovals, polar system of coordinates, coordinate families, groups of symmetries, curvilinear symmetries
Citation in English: Rakcheeva T.A. Polypolar coordination and symmetries // Computer Research and Modeling, 2010, vol. 2, no. 4, pp. 329-341
Citation in English: Rakcheeva T.A. Polypolar coordination and symmetries // Computer Research and Modeling, 2010, vol. 2, no. 4, pp. 329-341
DOI: 10.20537/2076-7633-2010-2-4-329-341
URL: http://crm-en.ics.org.ru/journal/article/1743/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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