Matsyuk, R.Ya.
Variatonality of geodesic circles in two dimensions. (English) Zbl 1158.70006
Kowalski, Oldřich (ed.) et al., Differential geometry and its applications. Proceedings of the 10th international conference on differential geometry and its applications, DGA 2007, Olomouc, Czech Republic, August 27–31, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-279-060-6/hbk). 635-642 (2008).

Summary: This note treats the notion of Lagrange derivative for the third-order mechanics in the context of covariant Riemannian geometry. We obtain the variational differential equation for geodesic cricles in two dimensions. The influence of the curvature tensor on the Lagrange derivative leads to the emergence of the quasiclassical spin in the pseudo-Riemannian case.

For the entire collection see [Zbl 1154.53003].

MSC:
70G45 Differential-geometric methods for dynamical systems
70H50 Higher-order theories (mechanics of particles and systems)
Keywords:
Lagrange derivative; covariant Riemannian geometry; curvature tensor; quasiclassical spin