{"title":"A Note on the Objectivity (Rotational Invariance) of the Stored Energy Density in Continuum Physics","authors":"Jiashi Yang","doi":"arxiv-2409.07478","DOIUrl":null,"url":null,"abstract":"This short note is concerned with the rotational invariance of the stored\nenergy density in continuum physics as a scalar function of a few vectors. A\nsimple derivation is presented for the determination of the general form of the\nenergy density in the case of a two-dimensional space. It is also shown that\nthe general form of the energy density so determined may be further reduced.\nThe three-dimensional case is also discussed.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Classical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07478","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This short note is concerned with the rotational invariance of the stored
energy density in continuum physics as a scalar function of a few vectors. A
simple derivation is presented for the determination of the general form of the
energy density in the case of a two-dimensional space. It is also shown that
the general form of the energy density so determined may be further reduced.
The three-dimensional case is also discussed.
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