PURSUE OF A FUGITIVE UNDER THE CONDITIONS OF HIS BRACHISTOCRONIC MOTION IN A FLAT VECTOR FIELD
DOI:
https://doi.org/10.35546/kntu2078-4481.2026.2.34Keywords:
fugitive, pursuer, starting and finishing points, pursuit process, interception, optimal trajectory,Abstract
The current problem of studying the process of pursuing a fugitive who escapes along a brachistochronous trajectory in a flat vector field was solved. The brachistochronous trajectory of the fugitive was determined using variational methods, based on the criterion of the minimum time spent on moving between the starting and finishing points. In addition, the optimality of choosing the finishing point was considered in the sense of the maximum horizontal movement of the fugitive in the direction of the “life line”. It was assumed that the pursuer at each moment of time tries to move along an instantaneous line that visually connects two current points (his and the fugitive) on a horizontal plane, i.e. the pursuer during the pursuit “keeps a course for the fugitive”. The fugitive's goal is to advance as far as possible in the direction of the "life line" until the moment of his interception by the pursuer, choosing the optimal finish point on the "life line". In turn, the pursuer tries to catch up with the fugitive before he has time to reach a certain point located on the "life line". To study the pursuit process, a mathematical model was built in the form of a system of four first-order differential equations. A method for numerically solving the resulting system of equations was developed, which allowed determining the equation of the optimal escape trajectory. Based on numerical analysis, the influence of the parameters of the pursuit process on the shape of the pursuit and escape curves was clarified. The dependence of the change in the horizontal movement of the fugitive towards the "life line" until the moment of his capture was established depending on the choice of the finish point on the "life line". It is shown that this dependence has a clearly expressed local maximum, which indicates the existence of a certain finish point on the "life line", which provides the fugitive with the opportunity to achieve maximum horizontal advancement towards the "life line" until the moment of interception
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