New and old parameterizations of the Cassinian ovals and some applications of them

DOI10.7546/giq-23-2022-75-98OpenAlexW4225620619MaRDI QIDQ6158493

Ivaïlo M. Mladenov

Publication date: 31 May 2023

Published in: Geometry, Integrability and Quantization (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/geometry-integrability-and-quantization-papers-and-lecture-series/volume-23/issue-none/New-and-Old-Parameterizations-of-the-Cassinian-Ovals-and-Some/10.7546/giq-23-2022-75-98.full

zbMATH Keywords

Cassinian ovalidentities between Jacobian elliptic functionsuniversal formula for the area of the Cassiniansvolumes of the rotated Cassinians

Mathematics Subject Classification ID

Integration of real functions of several variables: length, area, volume (26B15) Length, area and volume in real or complex geometry (51M25) Curves in Euclidean and related spaces (53A04)

Related Items (4)

Explicit solution of the focus locus problem for the harmonic oscillator orbits in the plane ⋮ Numerical ranges of the real \(2\times 2\) matrices derived by first principles ⋮ Geometry of the ovoids: avian eggs and similar asymmetric forms ⋮ Analytical descriptions of Perseus spirics

Cites Work

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• Cassini curves in light field theory
• Cassini ovals in harmonic motion orbits
• The many faces of elastica
• The spiric sections of Perseus and the uniform parameterizations of the Cassinian ovals
• Analytical descriptions of Perseus spirics
• The rectifications of the Cassinian ovals: third round
• On Some Deformations of the Cassinian Oval
• Cassini Ovals Associated with a Second Order Matrix

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