English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In the present paper, the nonlinear differential equation of pendulum isinvestigated to find an exact closed form solution, satisfying governingequation as well as initial conditions. The new concepts used in the suggestedmethod are introduced. Regarding the fact that the governing equation for anyarbitrary system represents its inherent properties, it is shown that thenonlinear term causes that the system to have a variable identity. Hence, theoriginal function is included as a variable in the solution to can take intoaccount the variation of governing equation. To find the exact closed formsolution, the variation of the nonlinear differential equation tends to zero,where in this case the system with a local linear differential equation has adefinite identity with a definite local answer. It is shown that the generalanswer is an arbitrary curve on a surface, a newly developed concept known assuper function, and different initial conditions give different curves asparticular solutions. The comparison of the results with those of finitedifference shows an exact agreement for any arbitrary amplitude and initialconditions.

A General Exact Closed-Form Solution for Nonlinear Differential Equation of Pendulum