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math.GM2021
Exact Solutions of the Cubic-Quintic Duffing Equation Using Leaf Functions
Kazunori Shinohara
The exact solutions of both the cubic Duffing equation and cubic-quintic Duffing equation are presented by using only leaf functions. In previous studies, exact solutions of the cu…
math.GM2020
Lemniscate of Leaf Function
Kazunori Shinohara
A lemniscate is a curve defined by two foci, F1 and F2. If the distance between the focal points of F1 - F2 is 2a (a: constant), then any point P on the lemniscate curve satisfy th…
math.GM2017
Exact Solutions to Cubic Duffing Equation by Leaf Functions Under Free Vibration
Kazunori Shinohara
Exact solutions with the initial conditions are presented in the cubic duffing equation. These exact solutions are expressed in terms of the leaf function and the trigonometric fun…