KFU. Card publication. Development of the numerical approach in the theory of physical libration within the framework of the “main problem”

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DEVELOPMENT OF THE NUMERICAL APPROACH IN THE THEORY OF PHYSICAL LIBRATION WITHIN THE FRAMEWORK OF THE &LDQUO;MAIN PROBLEM&RDQUO;

Form of presentation

Articles in Russian journals and collections

Year of publication

2017

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Authors, employees of KFU

Glushkov Maksim Vadimovich, author

Zagidullin Artur Aleksandrovich, author

Nefedev Yuriy Anatolevich, author

Petrova Natalya Konstantinovna, author

Usanin Vladimir Sergeevich, author

Bibliographic description in the original language

Zagidullin A.A., Petrova N.K., Usanin V.S., Nefediev Yu.A., Glushkov M.V. Development of the numerical approach in the theory of physical libration within the framework of the “main problem” // Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki (Proceedings of Kazan University. Physics and Mathematics Series). – 2017. – V. 159, No 4. – P. 529–546. (In Russian)

Annotation

A numerical theory of lunar rotation has been developed. The mathematical model of the rotation of the Moon has been considered within the “main problem”. The equations of the rotation have been constructed on the basis of the Hamiltonian approach. The resulting differential equations have been solved using the 10th order Runge–Kutta method. The analysis of the obtained data has been carried out on the basis of residual differences (between the numerical and analytical solutions). As a result, we have found that the range of residual differences does not exceed in modulus 1.8 and 0.9 arcsec. by longitude and latitude, respectively. This relatively high divergence occurs due to the fact that the frequencies are close to the natural frequencies of the system.

Keywords

theory of physical libration of Moon, main problem, Hamilton's equations, Runge-Kutta method, residual differences, resonant frequencies

The name of the journal

Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki

URL

https://kpfu.ru/development-of-the-numerical-approach-in-the_336178.html

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=183142&p_lang=2

Resource files

File name	Size (MB)	Format
F_159_4_phys_mat_9.pdf	1,12	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Glushkov Maksim Vadimovich	ru_RU
dc.contributor.author	Zagidullin Artur Aleksandrovich	ru_RU
dc.contributor.author	Nefedev Yuriy Anatolevich	ru_RU
dc.contributor.author	Petrova Natalya Konstantinovna	ru_RU
dc.contributor.author	Usanin Vladimir Sergeevich	ru_RU
dc.date.accessioned	2017-01-01T00:00:00Z	ru_RU
dc.date.available	2017-01-01T00:00:00Z	ru_RU
dc.date.issued	2017	ru_RU
dc.identifier.citation	Zagidullin A.A., Petrova N.K., Usanin V.S., Nefediev Yu.A., Glushkov M.V. Development of the numerical approach in the theory of physical libration within the framework of the “main problem” // Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki (Proceedings of Kazan University. Physics and Mathematics Series). – 2017. – V. 159, No 4. – P. 529–546. (In Russian)	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=183142&p_lang=2	ru_RU
dc.description.abstract	Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki	ru_RU
dc.description.abstract	A numerical theory of lunar rotation has been developed. The mathematical model of the rotation of the Moon has been considered within the “main problem”. The equations of the rotation have been constructed on the basis of the Hamiltonian approach. The resulting differential equations have been solved using the 10th order Runge–Kutta method. The analysis of the obtained data has been carried out on the basis of residual differences (between the numerical and analytical solutions). As a result, we have found that the range of residual differences does not exceed in modulus 1.8 and 0.9 arcsec. by longitude and latitude, respectively. This relatively high divergence occurs due to the fact that the frequencies are close to the natural frequencies of the system.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	theory of physical libration of Moon	ru_RU
dc.subject	main problem	ru_RU
dc.subject	Hamilton's equations	ru_RU
dc.subject	Runge-Kutta method	ru_RU
dc.subject	residual differences	ru_RU
dc.subject	resonant frequencies	ru_RU
dc.title	Development of the numerical approach in the theory of physical libration within the framework of the “main problem”	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU