Fifth-order AGM-formula for the period of a large-angle pendulum
نویسندگان
چکیده
In this paper, an approximate algebraic formula for calculating the period of a large-angle pendulum was developed based on fifth-order iteration arithmetic-geometric mean (AGM) complete elliptic integral first kind. The present is capable estimating nonlinear entire range possible amplitudes i.e. 0∘<A<180∘, but it particularly useful (90∘<A≤170∘) and extremely (170∘<A≤179.9∘) oscillations. accuracy tested using exact solution, numerical solution other published formulas. It observed that several orders more accurate than maximum error up to 179.9∘ found be 2.93×10-6%. can used pedagogical purpose because its simplicity.
منابع مشابه
An accurate formula for the period of a simple pendulum oscillating beyond the small angle regime
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15 صفحه اولAn Explicit Formula for the Genus 3 Agm
Given a smooth non-hyperelliptic curve C of genus 3 and a maximal isotropic subgroup (w.r.t. the Weil pairing) L ⊂ Jac(C)[2], there exists a smooth curve C′ s.t. Jac(C′) = Jac(C)/L. This construction is symmetric. i.e. if we start with C′ and the dual flag on it, we get C. A previous less explicit approach was taken by Donagi and Livné (see [DL]). The advantage of our construction is that it is...
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ژورنال
عنوان ژورنال: Revista Brasileira de Ensino de Física
سال: 2023
ISSN: ['1806-1117', '1806-9126']
DOI: https://doi.org/10.1590/1806-9126-rbef-2023-0014