On an analytical solution of the optimum trajectory problem in a gravitational field |
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| Authors: | A G Azizov N A Korshunova |
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| Institution: | (1) Tashkent State University, Tashkent, U.S.S.R. |
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| Abstract: | Mayer's variational problem for a point with a limited mass flow rate is described by differential equations of the fourteenth order, allowing for a few first integrals. By reducing the equations to closed canonical form, these integrals are analyzed from the viewpoint of finding a possible solution to the problem via quadratures on zero, intermediate, and maximum thrust sections. In addition to confirming well-known cases of total integrability, this approach enabled us to establish that the essential difficulty of the solution of the space problem with intermediate thrust is reduced to finding one integral, and the solution of the problem with maximum thrust requires two integrals in involution. It is shown that these integrals can be applied to find particular solutions. |
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