Geodesic
On a nonlinear isochronous system
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 59-63 
V. M. Budanov. On a nonlinear isochronous system. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 59-63. http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a12/
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     title = {On a nonlinear isochronous system},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A system of nonlinear ordinal differential equations of second order is considered. It is shown analytically that the solutions of this system are isochronous, which is not characteristic for nonlinear systems. It is also shown that the periodic delta-function is a limiting case for the solution if the amplitude tends to infinity.

[1] Chaplygin S.A., “K teorii dvizheniya negolonomnykh sistem, teorema o privodyaschem mnozhitele”, Matem. sb., 28:2 (1911), 303–314

[2] Budanov V.M., Devyanin E.A., “O dvizhenii kolesnykh robotov”, Prikl. matem. i mekhan., 67:2 (2003), 244–255 | MR

[3] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie sistemy i bifurkatsii vektornykh polei, M.–Izhevsk, 2002

[4] Andronov A.A., Leontovich E.A., Gordon I.I., Maier A.G., Kachestvennaya teoriya dinamicheskikh sistem vtorogo poryadka, Nauka, M., 1966 | MR