Geodesic
Brachystochronous movement on a manifold
Theoretical and applied mechanics, Tome 24 (1998) no. 1, p. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The paper presents an analysis of brachystochronous movement of a conservative system during the action of holonomous relations. More precisely, it deals with solving the assignment of moving a system on a configurational manifold from one given position, where it remains at rest, to another given position, for the shortest possible time. The differential equations of this movement are formulated, and several special cases are analyzed. The geometrical characteristics of the regions of the possible brachystochronous movements are also indicated. 
@article{TAM_1998_24_1_a0,
     author = {Aleksandar Bak\v{s}a},
     title = {Brachystochronous movement on a  manifold},
     journal = {Theoretical and applied mechanics},
     pages = {1 },
     year = {1998},
     volume = {24},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1998_24_1_a0/}
}
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Aleksandar Bakša. Brachystochronous movement on a  manifold. Theoretical and applied mechanics, Tome 24 (1998) no. 1, p. 1 . http://geodesic.mathdoc.fr/item/TAM_1998_24_1_a0/