Geodesic
Development of the numerical approach in the theory of physical libration within the framework of the “main problem”
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 529-546

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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. 
@article{UZKU_2017_159_4_a8,
     author = {A. A. Zagidullin and N. K. Petrova and V. S. Usanin and Yu. A. Nefediev and M. V. Glushkov},
     title = {Development of the numerical approach in the theory of physical libration within the framework of the {\textquotedblleft}main problem{\textquotedblright}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {529--546},
     publisher = {mathdoc},
     volume = {159},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a8/}
}
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A. A. Zagidullin; N. K. Petrova; V. S. Usanin; Yu. A. Nefediev; M. V. Glushkov. Development of the numerical approach in the theory of physical libration within the framework of the “main problem”. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 529-546. http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a8/