7 citations · 9 across the 3 of their papers we have counts for
6 papers
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…
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…
Pendulum Analysis by Leaf Functions and Hyperbolic Leaf Functions
Kazunori Shinohara
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as tr…
Addition formulas of Leaf Functions and Hyperbolic Leaf Functions
Kazunori Shinohara
Addition formulas exist in trigonometric functions. Double-angle and half-angle formulas can be derived from these formulas. Moreover, the relation equation between the trigonometr…
Damped and Divergence Exact Solutions for the Duffing Equation using Leaf Functions and Hyperbolic Leaf Functions
Kazunori Shinohara
According to the wave power rule, the second derivative of a function with respect to the variable t is equal to negative n times the function raised to the power of 2n-1. Solving…
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…