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As an application, we prove an extension of Asimow and Roth\u2019s 1978\/1979 result establishing the equivalence of local, continuous and infinitesimal rigidity for regular bar-and-joint frameworks in a <jats:italic>d<\/jats:italic>-dimensional Euclidean space. Further, we obtain upper bounds for the dimension of the space of trivial motions for a framework and establish the flexibility of small frameworks in general non-Euclidean normed spaces.<\/jats:p>","DOI":"10.1007\/s00454-019-00135-5","type":"journal-article","created":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T16:17:32Z","timestamp":1568996252000},"page":"655-679","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2220-4576","authenticated-orcid":false,"given":"Sean","family":"Dewar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,9,20]]},"reference":[{"key":"135_CR1","volume-title":"Foundations of Mechanics","author":"R Abraham","year":"1978","unstructured":"Abraham, R., Marsden, J.E.: Foundations of Mechanics, 2nd edn. 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