Geodesic
Geometry of classical mechanics with non-Abelian gauge symmetry
Teoretičeskaâ i matematičeskaâ fizika, Tome 73 (1987) no. 1, pp. 3-15

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Geometry of the gauge orbit bundle is considered for the $SO(3)$ Yang–Mills mechanics. It is shown that it may serve as a finite-dimensional model of the geometry of nonabelian field theory with respect to such properties as the nonexistence of a global gauge, the Gribov ambiguities, convexity of the region within the corresponding horizon and stratification. The connection and the Lagrangian on the orbit space are obtained. 
@article{TMF_1987_73_1_a0,
     author = {M. A. Soloviev},
     title = {Geometry of classical mechanics with {non-Abelian} gauge symmetry},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {73},
     number = {1},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_73_1_a0/}
}
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M. A. Soloviev. Geometry of classical mechanics with non-Abelian gauge symmetry. Teoretičeskaâ i matematičeskaâ fizika, Tome 73 (1987) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/TMF_1987_73_1_a0/