Geodesic
The convergence of Euler's broken lines
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 163-164

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We consider the convergence of Euler's broken lines to trajectories of the system under Carathéodory's conditions. We introduce a pseudometric on the set of closed subsets of the time segment, taking into account the system. We prove that the convergence of partitions guarantees the convergence of Euler's broken lines to the funnel of solutions of the system. 
@article{VUU_2008_2_a52,
     author = {D. V. Khlopin},
     title = {The convergence of {Euler's} broken lines},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {163--164},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2008_2_a52/}
}
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D. V. Khlopin. The convergence of Euler's broken lines. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 163-164. http://geodesic.mathdoc.fr/item/VUU_2008_2_a52/