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- W4385981394 abstract "A new approach to solving the Zermelo navigation problem using variational methods is proposed, which differs from methods based on the Pontryagin maximum principle. In this work, the motion of the ship is presented as the motion of a material point in a flat horizontal vector field of a moving fluid, for which the classic variational problem of finding brachistochronous trajectories is formulated. The purpose of the work is to establish the equations of brachistochronous trajectories of the movement of a material point, which ensure the minimum time of its movement between two given points The objective function of the time of movement of a material point between given points is constructed, which is then minimized. With its use, Euler’s equation was obtained, which allows us to directly write the differential equations of extreme trajectories. Algebraic equations of the brachistochronous motion of a material point have been established for a given version of the boundary conditions using numerical experiments. A comparative analysis of the time spent both on extreme trajectories and on an alternative straight path was carried out. It is established that the given variational problem generates two solutions of opposite sign, and only one of them delivers the minimum of the time functional. A comparative analysis of the calculation results showed that the brachistochronous trajectory of the movement of a material point is not a straight line connecting two given points, but is an oscillating curve." @default.
- W4385981394 created "2023-08-19" @default.
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- W4385981394 date "2023-01-01" @default.
- W4385981394 modified "2023-10-14" @default.
- W4385981394 title "Determination of Brachistochronous Trajectories of Movement of a Material Point in a One-Dimensional Vector Field" @default.
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- W4385981394 doi "https://doi.org/10.1007/978-3-031-36118-0_63" @default.
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