 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 77, Issue 2 / 2013 | Next article >> |
| A.N. Sirotin, "A family of trigonometric extremals in the problem of reorienting a spherically symmetrical body with minimum energy consumption," J. Appl. Math. Mech. 77 (2), 205-211 (2013) |
| Year |
2013 |
Volume |
77 |
Issue |
2 |
Pages |
205-211 |
| Title |
A family of trigonometric extremals in the problem of reorienting a spherically symmetrical body with minimum energy consumption |
| Author(s) |
A.N. Sirotin (Moscow, Russia, asirotin2@yandex.ru) |
| Abstract |
The problem of the optimal control of the reorientation of an absolutely rigid, spherically symmetric body is investigated. An integral quadratic functional, which characterizes the total energy consumption, is chosen as the criterion of the efficiency of the manoeuvre. The resultant torque of the applied external forces serves as the control. Application of the formalism of the Pontryagin's maximum principle leads to an analysis of a third-order non-linear vector differential equation, whose general solution is still unknown at the present time. It is shown that this equation has a particular solution described by trigonometric functions of time, which can be used to completely reconstruct the explicit solution for the corresponding extremal rotation. An analogy with the free rotation of a certain axisymmetric body is proposed. |
| Received |
20 December 2011 |
| Link to Fulltext |
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