The quickest transfer of a spatial dynamic object into a circular domain |
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| Authors: | LD Akulenko |
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| Institution: | 1. Graduate Program in Natural Resource Engineering in the Amazon, PRODERNA/ITEC/UFPA, Universidade Federal do Pará, 66075-110 Belém, PA, Brazil;2. Dept. of Mechanical Engineering, COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Cx. Postal 68503, Cidade Universitária, Rio de Janeiro, RJ 21945-970, Brazil;3. Araguaia Institute of Engineering, IEA/UNIFESSPA, Universidade do Sul e Sudeste do Pará, Campus Santana do Araguaia, Bel Recanto, Rua Albino Malzoni, 68560-000 Santana do Araguaia, PA, Brazil;4. School of Chemical Engineering, FEQ/ITEC/UFPA, Universidade Federal do Pará, Campus Universitário do Guamá, 66075-110 Belém, PA, Brazil;1. Health Services Department, School of Public Health, University of California, Los Angeles, Los Angeles, CA, USA;2. Department of Neurology, University of California at Irvine, Irvine, CA, USA |
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| Abstract: | The spatial problem of the time-optimal transfer of a point mass by a limited force onto a terminal set in the form of a circle without fixing the final velocity is investigated. The optimal modes of motion are constructed and investigated for arbitrary initial values of the three-dimensional position and velocity vectors using the maximum principle. The governing relations are obtained in the form of fourth-order and eighth-order algebraic equations for the minimum time of motion, which enable the dependence on the initial data to be investigated constructively. The qualitative features of the solution due to a jump discontinuity in the minimum time of motion, which lead to jumps in the control vector, are established. The problem is solved approximately by perturbation methods for the cases of motion close to singular ones. A complete investigation of the control problem for the motion of an object in the plane of a circle and close to it is presented using an original numerical-analytical approach. |
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