Some Generalized Trigonometric Sine Functions and Their Applications
Loading...
Date
2012
Authors
Wei, Dongming
Liu, Yu
Journal Title
Journal ISSN
Volume Title
Publisher
Applied Mathematical Sciences
Abstract
In this paper, it is shown that D. Shelupsky's generalized sine func-
tion, and various general sine functions developed by P. Drabek, R.
Manasevich and M. Otani, P. Lindqvist, including the generalized Ja-
cobi elliptic sine function of S. Takeuchi can be defned by systems of
first order nonlinear ordinary differential equations with initial condi-
tions. The structure of the system of differential equations is shown to
be related to the Hamilton System in Lagrangian Mechanics. Numer-
ical solutions of the ODE systems are solved to demonstrate the sine
functions graphically. It is also demonstrated that the some of the gen-
eralized sine functions can be used to obtain analytic solutions to the
equation of a nonlinear spring-mass system.
Description
Keywords
generalized sine, Hamilton system, nonlinear spring, vibration, analytic solution
Citation
Dongming Wei and Yu Liu; 2012; Some Generalized Trigonometric Sine Functions and Their Applications; Applied Mathematical Sciences; http://nur.nu.edu.kz/handle/123456789/1915