Articles

Permanent URI for this collection

https://testres.nu.edu.kz/handle/123456789/904

Browse

Browsing Articles by Subject "analytic solution"

Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    Some Generalized Trigonometric Sine Functions and Their Applications
    (Applied Mathematical Sciences, 2012) Wei, Dongming; Liu, Yu
    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.