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Families of ovals and their orthogonal trajectories

Published online by Cambridge University Press:  01 August 2016

D. F. Lawden*
Affiliation:
Church Bank, Temple Grafton, Alcester B49 6NU

Extract

Ann Hirst and Keith Lloyd have derived many interesting properties of the Cassini ovals rr′ = a2, r and r′ being the distances of a variable point P from two fixed points A and B, which we shall find it convenient to take a unit distance apart. r, r′ are often referred to as bipolar coordinates and by relating them in different ways, a variety of interesting families of curves can be defined; such families can be associated with other families which are their orthogonal trajectories. The purpose of this article is to draw attention to a number of such cases.

Type
Articles
Copyright
Copyright © The Mathematical Association 1999

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References

1. Hirst, Ann and Lloyd, Keith Cassini, his ovals and a space probe to Saturn, Math. Gaz. 81 (November 1997) pp. 409421.Google Scholar
2. Lawden, D. F. Electromagnetism, Allen & Unwin (1973).Google Scholar
3. Jeans, Jame Sir Mathematical theory of electricity and magnetism, Cambridge (1933).Google Scholar
4. Lockwood, E. H. A book of curves, Cambridge (1961).Google Scholar
5. Lawden, D. F. Elliptic functions and applications, Springer (1989).Google Scholar