Geodesic
Two-point boundary value problems in relativistic dynamics
Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 437-449

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For gyro systems of relativistic type, we obtain solvability conditions for the two-point boundary value problem. We use the geodesic modeling method, in which the original problem is reduced to studying the existence of isotropic geodesic curves of the Kaluts–O. Klein Lorentz metric joining two fibers of a bundle over the configuration manifold of the system. As an example, we consider problems on the motion of charged test particles in an arbitrary electromagnetic field and in the outer Reissner–Nordstrem space-time in the field of a charged black hole and some external electromagnetic field. 
@article{MZM_1996_59_3_a12,
     author = {E. I. Yakovlev},
     title = {Two-point boundary value problems in relativistic dynamics},
     journal = {Matemati\v{c}eskie zametki},
     pages = {437--449},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a12/}
}
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E. I. Yakovlev. Two-point boundary value problems in relativistic dynamics. Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 437-449. http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a12/