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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…
math.FA2017★ 7 cited
Addition Formulas of Leaf Functions According to Integral Root of Polynomial Based on Analogies of Inverse Trigonometric Functions and Inverse Lemniscate Functions
Kazunori Shinohara
The second derivative of a function r(t) with respect to a variable t is equal to -n times the function raised to the 2n-1 power of r(t); using this definition, an ordinary differe…