The geodesic deviation equations, called also the Jacobi equations, describe only the first-order effects, linear in the small parameter characterizing the deviation from an original worldline. They can be easily generalized if we take into account the higher-order terms. Here we derive these higher-order equations not only directly, but also from the Taylor expansion of the variational principle itself. Then we show how these equations can be used in a novel approach to the two-body problem in General Relativity
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc59-0-9,
author = {R. Kerner},
title = {Generalized geodesic deviations: a Lagrangean approach},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {173-188},
zbl = {1026.83015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc59-0-9}
}
R. Kerner. Generalized geodesic deviations: a Lagrangean approach. Banach Center Publications, Tome 60 (2003) pp. 173-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc59-0-9/