Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..38..297a&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 38, April 1986, p. 297-306.
Astronomy and Astrophysics
Astronomy
2
Astrodynamics, Gravitational Fields, Trajectory Optimization, Canonical Forms, Differential Equations, Quadratures
Scientific paper
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 made it possible 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.
Azizov A. G.
Korshunova N. A.
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