Matsyuk, Roman Ya.
The variational principle for the uniform acceleration and quasi-spin in two dimensional space-time. (English) Zbl 1133.53017
SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 016, 11 p., electronic only (2008).
Summary: The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are discovered. The relationship with the physical notion of uniformly accelerated relativistic particles 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.

MSC:
53B50 Applications of local differential geometry to physics
53C27 Spin and Spin c geometry
70H50 Higher-order theories (mechanics of particles and systems)
49N45 Inverse problems in calculus of variations
83C10 Equations of motion