On a Generalized Superellipse: From Models to Applications

ABSTRACT

This study is concerned with a power‐form functional equation and its various forms in Cartesian and polar coordinates. An overview of the related contributions is presented and illustrated in terms of the shapes that they can yield, thereby establishing cross‐disciplinary phenomenological links by demonstrating the application of identical mathematical models across diverse fields within nonlinear science, marking a novel approach in this context. Finally, an analytical solution of this equation is elaborated both with respect to its form as a functional equation and as a Hamiltonian function. The original solutions in terms of trigonometric or generalized trigonometric functions are presented as well.