Abstract:
In this paper, we consider the minimum time problem for a space rocket whose
dynamics is given by a control-affine system with drift. The admissible control set is a disc. We
study extremals in the neighbourhood of singular points of the second order. Our approach is
based on applying the method of a descending system of Poisson brackets and the Zelikin –
Borisov method for resolution of singularities to the Hamiltonian system of Pontryagin’s
maximum principle. We show that in the neighbourhood of any singular point there is a family
of spiral-like solutions of the Hamiltonian system that enter the singular point in a finite time,
while the control performs an infinite number of rotations around the circle.
Keywords:
Hamiltonian system of Pontryagin’s maximum principle, singular extremal, control-affine system with drift, descending system of Poisson brackets, resolution of singularity, blow-up, coupled attitude orbit problem.
Citation:
Mariya I. Ronzhina, Larisa A. Manita, “Spiral-Like Extremals near a Singular Surface
in a Rocket Control Problem”, Regul. Chaotic Dyn., 28:2 (2023), 148–161
\Bibitem{RonMan23}
\by Mariya I. Ronzhina, Larisa A. Manita
\paper Spiral-Like Extremals near a Singular Surface
in a Rocket Control Problem
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 2
\pages 148--161
\mathnet{http://mi.mathnet.ru/rcd1199}
\crossref{https://doi.org/10.1134/S1560354723020028}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4572230}
Linking options:
https://www.mathnet.ru/eng/rcd1199
https://www.mathnet.ru/eng/rcd/v28/i2/p148
This publication is cited in the following 5 articles:
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