Features of the mathematical model of the interaction between track and rolling stock within the switch

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In this work the peculiarities of mathematical modeling of interaction of rail vehicles and switches when moving onto a side track are given. The mathematical model of interaction taking into account the given peculiarities of switch side direction is developed and approved.

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[1.3/(] / Q. 0. ,=,M3, // P.G<HD. /;. )4H@. (+.

/ 0""1. – 1967. – <K*. 78. – R. 18-27.

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-/,<KFL3>*4G.: [1.3/(] / . . ],<,+HF4. – $.:

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– 1985. – <K*. 4. – R. 62-68.

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1992. – 45 /.

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P. ^. .+>A,, . _. N.<D).+ // R;. )4H@. (+. /

&""b1. – 1969. – <K*. 385. – R. 95-106.

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*+,&0! / Q. 0. ,=,M3,, 7. N. 14(H+.<>@. –

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