Some generalized trigonometric sine functions and their applications

Dongming Wei, Yu Liu, Mohamed Elgindi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, it is shown that D. Shelupsky's generalized sine function, and various general sine functions developed by P. Drábek, R. Manásevich and M. Ôtani, P. Lindqvist, including the generalized Jacobi elliptic sine function of S. Takeuchi can be dened by systems of rst order nonlinear ordinary differential equations with initial conditions. The structure of the system of differential equations is shown to be related to the Hamilton System in Lagrangian Mechanics. Numerical solutions of the ODE systems are solved to demonstrate the sine functions graphically. It is also demonstrated that the some of the generalized sine functions can be used to obtain analytic solutions to the equation of a nonlinear spring-mass system.

Original languageEnglish
Pages (from-to)6053-6068
Number of pages16
JournalApplied Mathematical Sciences
Volume6
Issue number121-124
Publication statusPublished - 2012

Fingerprint

Lagrangian Mechanics
Nonlinear Ordinary Differential Equations
System of Differential Equations
Analytic Solution
Ordinary differential equations
Jacobi
Mechanics
Initial conditions
Differential equations
Numerical Solution
Demonstrate
Graphics

Keywords

  • Analytic solution
  • Generalized sine
  • Hamilton system
  • nonlinear spring
  • Vibration

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Some generalized trigonometric sine functions and their applications. / Wei, Dongming; Liu, Yu; Elgindi, Mohamed.

In: Applied Mathematical Sciences, Vol. 6, No. 121-124, 2012, p. 6053-6068.

Research output: Contribution to journalArticle

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