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Title:Variationality of geodesic circles in two dimensions
DOI No:10.1142/9789812790613_0053
Source:DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS (pp 635-642)
Copyright:World Scientific Publishing Co. Pte. Ltd.
Author(s):R. Ya. Matsyuk
Institute for Applied Problems in Mechanics and Mathematics, 15 Dudayev St., L'viv, 79005, Ukraine

Abstract:This note treats the notion of Lagrange derivative for the third order mechanics in the context of covariant Riemannian geometry. The variational differential equation for geodesic circles in two dimensions is obtained. The influence of the curvature tensor on the Lagrange derivative leads to the emergence of the notion of quasiclassical spin in the pseudo-Riemannian case.
Keywords:Ostrohrads'kyj mechanics; inverse variational problem; concircular geometry; classical spin
AMSC numbers: 53A40, 70H50, 49N45, 83C10
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