立方平均のソースを表示

'''立方平均''' (りっぽうへいきん、{{lang-en|Cubic mean}}、<math>\bar{x}_\mathrm{cubic}</math>)は、''p''=''3''の場合の[[ヘルダー平均]]である。材料の[[疲労 (材料)|疲労]]による寿命の予測に使われる<ref name=equiv-load/><ref>{{cite web|title=ISO 4301-1-1986 Cranes and lifting appliances; Classification; Part 1 : General|year=1986|url=http://www.iso.org/iso/catalogue_detail.htm?csnumber=10151 |website=www.iso.org|accessdate=2021-12-12}} also available from {{cite web|url=http://www.freestd.us/soft/17753.htm|title=freestd.us|accessdate=2015-01-20}}</ref><ref>{{cite book|last1=Babu & Sridhar|title=Design of Machine Elements|year=2010|isbn=9780070672840|url=https://books.google.com/books?id=Px9kbvsG3WYC&q=cubic+mean+load&pg=PA354|accessdate=2015-01-20}}</ref><ref>{{cite book|title=Essential Concepts of Bearing Technology, Fifth Edition|isbn = 9781420006599|url=https://books.google.com/books?id=0XYE2p0QyFwC&q=cubic+mean+load&pg=PA230|accessdate=2015-01-20|last1 = Harris|first1 = Tedric A.|last2 = Kotzalas|first2 = Michael N.|date = 9 October 2006}}</ref>。

==定義==
n個の[[実数]]''x<sub>i</sub>''の立方平均は<math>\sqrt[3]{\frac{1}{n}\sum_{i=1}^n{x_i^3}} = \sqrt[3]{{x_1^3 + x_2^3 + \cdots + x_n^3} \over n}</math>である<ref>{{cite web|title=calculation formulas|url=http://prmeh.ru/pub/catalogues/skf/data/skf_products/linear_motion/screws/calculation_formules.pdf|accessdate=2021-12-12}}</ref><ref>{{cite book|last1=Svarovski|first1=Ladislav|title=Solid-Liquid Separation|date=31 October 2000|isbn=9780080541440|url=https://books.google.com/books?id=8dj5IJbEwu4C&q=cubic+mean+arithmetic+mean&pg=PA38}}</ref><ref name=equiv-load>{{cite web|title=Equivalent Load|url=http://www.creativemotioncontrol.com/home-copy/cmc-roller-screws/calculation-and-selection/equivalent-load/|website=Creative Motion Control|access-date=2015-01-19|archive-url=https://web.archive.org/web/20150120013504/http://www.creativemotioncontrol.com/home-copy/cmc-roller-screws/calculation-and-selection/equivalent-load/|archive-date=2015-01-20|url-status=dead}}</ref>。例えば、2個の実数''x<sub>1</sub>''と''x<sub>2</sub>''の立方平均は<math>\sqrt[3]{\frac{x_1^3+x_2^3}{2}}</math>となる。

==脚注==
{{Reflist}}
{{DEFAULTSORT:りつほうへいきん}}
[[Category:平均]]
[[Category:数学に関する記事]]