Geodesic
The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.
Keywords: covariant Ostrohrads'kyj mechanics; spin; concircular geometry; uniform acceleration. 
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Roman Ya. Matsyuk. The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a15/

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