Fast converging exact power series for the time and period of the simple pendulum

Fast converging exact power series for the time and period of the simple pendulum

A time explicit fast converging exact power series solution to the pendulum equation is derived in this paper. A novel series for the period results from it. The approximate formula that comprises the first three terms gives an accuracy of 99.99% up to the amplitude of 90°. The accuracy was compared...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:European journal of physics 2017-03, Vol.38 (2), p.25004
1. Verfasser: Benacka, Jan
Format: Artikel
Sprache:eng
Schlagworte:
period formula
power series solution
relative error
simple pendulum
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 2
container_start_page 25004
container_title European journal of physics
container_volume 38
creator Benacka, Jan
description A time explicit fast converging exact power series solution to the pendulum equation is derived in this paper. A novel series for the period results from it. The approximate formula that comprises the first three terms gives an accuracy of 99.99% up to the amplitude of 90°. The accuracy was compared with that of 11 other approximate period formulas.
doi_str_mv 10.1088/1361-6404/aa543f
format Article
fullrecord <record><control><sourceid>iop_cross</sourceid><recordid>TN_cdi_iop_journals_10_1088_1361_6404_aa543f</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>ejpaa543f</sourcerecordid><originalsourceid>FETCH-LOGICAL-c312t-95b8e55ec03a6535e66585d3a06f6814646e58aec851ea70fc8c48d5ccf49efb3</originalsourceid><addsrcrecordid>eNp9kM1LAzEUxIMoWKt3j7l5cTVpPpoepVgVCiLoOaTZl5qyuwlJ6sd_764VD6KeHgzzG94MQqeUXFCi1CVlklaSE35pjODM7aHRt7SPRoRyVhFFpofoKOcNIZQqykfoYWFywTZ0L5DWvltjeDO24BheIeEMyUPGLiRcngEX3wI2XY1jr4caB_cpZ9_GBnqxq7fNtj1GB840GU6-7hg9La4f57fV8v7mbn61rCyjk1LNxEqBEGAJM1IwAVIKJWpmiHSyf01yCUIZsEpQMFPirLJc1cJax2fgVmyMyC7XppBzAqdj8q1J75oSPUyih_566K93k_SI_IFYX0zxoSvJ-OY_8GwH-hD1JmxT1zfTsImaKT3RZCJIb4714Dz_xfln8AdDyoHU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Fast converging exact power series for the time and period of the simple pendulum</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><creator>Benacka, Jan</creator><creatorcontrib>Benacka, Jan</creatorcontrib><description>A time explicit fast converging exact power series solution to the pendulum equation is derived in this paper. A novel series for the period results from it. The approximate formula that comprises the first three terms gives an accuracy of 99.99% up to the amplitude of 90°. The accuracy was compared with that of 11 other approximate period formulas.</description><identifier>ISSN: 0143-0807</identifier><identifier>EISSN: 1361-6404</identifier><identifier>DOI: 10.1088/1361-6404/aa543f</identifier><identifier>CODEN: EJPHD4</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>period formula ; power series solution ; relative error ; simple pendulum</subject><ispartof>European journal of physics, 2017-03, Vol.38 (2), p.25004</ispartof><rights>2017 European Physical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c312t-95b8e55ec03a6535e66585d3a06f6814646e58aec851ea70fc8c48d5ccf49efb3</citedby><cites>FETCH-LOGICAL-c312t-95b8e55ec03a6535e66585d3a06f6814646e58aec851ea70fc8c48d5ccf49efb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1361-6404/aa543f/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,777,781,27905,27906,53827,53874</link.rule.ids></links><search><creatorcontrib>Benacka, Jan</creatorcontrib><title>Fast converging exact power series for the time and period of the simple pendulum</title><title>European journal of physics</title><addtitle>EJP</addtitle><addtitle>Eur. J. Phys</addtitle><description>A time explicit fast converging exact power series solution to the pendulum equation is derived in this paper. A novel series for the period results from it. The approximate formula that comprises the first three terms gives an accuracy of 99.99% up to the amplitude of 90°. The accuracy was compared with that of 11 other approximate period formulas.</description><subject>period formula</subject><subject>power series solution</subject><subject>relative error</subject><subject>simple pendulum</subject><issn>0143-0807</issn><issn>1361-6404</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kM1LAzEUxIMoWKt3j7l5cTVpPpoepVgVCiLoOaTZl5qyuwlJ6sd_764VD6KeHgzzG94MQqeUXFCi1CVlklaSE35pjODM7aHRt7SPRoRyVhFFpofoKOcNIZQqykfoYWFywTZ0L5DWvltjeDO24BheIeEMyUPGLiRcngEX3wI2XY1jr4caB_cpZ9_GBnqxq7fNtj1GB840GU6-7hg9La4f57fV8v7mbn61rCyjk1LNxEqBEGAJM1IwAVIKJWpmiHSyf01yCUIZsEpQMFPirLJc1cJax2fgVmyMyC7XppBzAqdj8q1J75oSPUyih_566K93k_SI_IFYX0zxoSvJ-OY_8GwH-hD1JmxT1zfTsImaKT3RZCJIb4714Dz_xfln8AdDyoHU</recordid><startdate>20170301</startdate><enddate>20170301</enddate><creator>Benacka, Jan</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170301</creationdate><title>Fast converging exact power series for the time and period of the simple pendulum</title><author>Benacka, Jan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c312t-95b8e55ec03a6535e66585d3a06f6814646e58aec851ea70fc8c48d5ccf49efb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>period formula</topic><topic>power series solution</topic><topic>relative error</topic><topic>simple pendulum</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Benacka, Jan</creatorcontrib><collection>CrossRef</collection><jtitle>European journal of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Benacka, Jan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fast converging exact power series for the time and period of the simple pendulum</atitle><jtitle>European journal of physics</jtitle><stitle>EJP</stitle><addtitle>Eur. J. Phys</addtitle><date>2017-03-01</date><risdate>2017</risdate><volume>38</volume><issue>2</issue><spage>25004</spage><pages>25004-</pages><issn>0143-0807</issn><eissn>1361-6404</eissn><coden>EJPHD4</coden><abstract>A time explicit fast converging exact power series solution to the pendulum equation is derived in this paper. A novel series for the period results from it. The approximate formula that comprises the first three terms gives an accuracy of 99.99% up to the amplitude of 90°. The accuracy was compared with that of 11 other approximate period formulas.</abstract><pub>IOP Publishing</pub><doi>10.1088/1361-6404/aa543f</doi><tpages>6</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0143-0807
ispartof European journal of physics, 2017-03, Vol.38 (2), p.25004
issn 0143-0807
1361-6404
language eng
recordid cdi_iop_journals_10_1088_1361_6404_aa543f
source IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link
subjects period formula
power series solution
relative error
simple pendulum
title Fast converging exact power series for the time and period of the simple pendulum
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-18T16%3A03%3A42IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-iop_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Fast%20converging%20exact%20power%20series%20for%20the%20time%20and%20period%20of%20the%20simple%20pendulum&rft.jtitle=European%20journal%20of%20physics&rft.au=Benacka,%20Jan&rft.date=2017-03-01&rft.volume=38&rft.issue=2&rft.spage=25004&rft.pages=25004-&rft.issn=0143-0807&rft.eissn=1361-6404&rft.coden=EJPHD4&rft_id=info:doi/10.1088/1361-6404/aa543f&rft_dat=%3Ciop_cross%3Eejpaa543f%3C/iop_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true