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Curvilinear coordinates
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==Vector and tensor algebra in three-dimensional curvilinear coordinates== {{Einstein_summation_convention}} Elementary vector and tensor algebra in curvilinear coordinates is used in some of the older scientific literature in [[mechanics]] and [[physics]] and can be indispensable to understanding work from the early and mid-1900s, for example the text by Green and Zerna.<ref name=Green>{{cite book | last1=Green | first1=A. E. | last2=Zerna | first2=W. | year=1968 | title=Theoretical Elasticity | publisher=Oxford University Press | isbn=0-19-853486-8 }}</ref> Some useful relations in the algebra of vectors and second-order tensors in curvilinear coordinates are given in this section. The notation and contents are primarily from Ogden,<ref name=Ogden00>{{cite book | last=Ogden | first=R. W. | year=2000 | title=Nonlinear elastic deformations | publisher=Dover}}</ref> Naghdi,<ref name=Naghdi>{{cite book | first1=P. M. | last1=Naghdi | year=1972 | contribution=Theory of shells and plates | editor=S. Flügge | title=Handbook of Physics | volume=VIa/2 | pages=425–640}}</ref> Simmonds,<ref name=Simmonds>{{cite book | last=Simmonds | first=J. G. | year=1994 | title=A brief on tensor analysis | publisher=Springer | isbn=0-387-90639-8}}</ref> Green and Zerna,<ref name=Green/> Basar and Weichert,<ref name=Basar>{{cite book | last1=Basar | first1=Y. | last2=Weichert | first2=D. | year=2000 | title=Numerical continuum mechanics of solids: fundamental concepts and perspectives | publisher=Springer}}</ref> and Ciarlet.<ref name=Ciarlet>{{cite book | last=Ciarlet | first=P. G. | year=2000 | title=Theory of Shells | volume=1 | publisher=Elsevier Science }}</ref>
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