Hostname: page-component-7bb8b95d7b-pwrkn Total loading time: 0 Render date: 2024-09-19T10:32:17.915Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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