Variatonality of geodesic circles in two
dimensions.
(English) Zbl 1158.70006Kowalski, 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) |