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.