Geodesic
On the results of the study of simplified systems in the problem of motion of four bodies in a plane
Problemy fiziki, matematiki i tehniki, no. 3 (2015), pp. 66-69.

Voir la notice de l'article provenant de la source Math-Net.Ru

The system describing the motion of four bodies in a plane is considered. The method of the small parameter of a simplified system consisting of non-linear differential equations, each of which has a second order is determined. For these systems, a set of interparticle interaction constants in which all its solutions of the system are meromorphic functions is specified.
Keywords: motion of four bodies in a plane, simple system, meromorphic function.
Mots-clés : interaction constant 
@article{PFMT_2015_3_a12,
     author = {A. T. Sazonova},
     title = {On the results of the study of simplified systems in the problem of motion of four bodies in a plane},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {66--69},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_3_a12/}
}
TY  - JOUR
AU  - A. T. Sazonova
TI  - On the results of the study of simplified systems in the problem of motion of four bodies in a plane
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 66
EP  - 69
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_3_a12/
LA  - ru
ID  - PFMT_2015_3_a12
ER  - 
%0 Journal Article
%A A. T. Sazonova
%T On the results of the study of simplified systems in the problem of motion of four bodies in a plane
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 66-69
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2015_3_a12/
%G ru
%F PFMT_2015_3_a12
A. T. Sazonova. On the results of the study of simplified systems in the problem of motion of four bodies in a plane. Problemy fiziki, matematiki i tehniki, no. 3 (2015), pp. 66-69. http://geodesic.mathdoc.fr/item/PFMT_2015_3_a12/

[1] F. Calogero, Classical Many-Body Problems amenable to exact treatments, Lect. Notes in Phys. Monograph, 66, Springer, Berlin, 2001, 749 pp. | DOI | MR | Zbl

[2] F. Calogero, J.-P. Françoise, “Periodic solutions of a many-rotator problem in the plane”, Inverse Problems, 17 (2001), 1–8 | DOI | MR

[3] F. Calogero, “Integrable and solvable many-body problems in the plane via complexification”, J. Math. Phys., 39 (1998), 5268–5291 | DOI | MR | Zbl

[4] F. Calogero, “Motion of poles and zeros of special solutions of nonlinear and linear partial differential equations and related “Solvable Many-Body Problems””, Nuovo Cimento, 43 B (1978), 177–241 | DOI | MR

[5] F. Calogero, J.-P. Françoise, M. Sommacal, “Periodic solutions of a many-rotator problem in the plane. II: Analysis of various motions”, J. Nonlinear Math. Phys., 10 (2003), 157–214 | DOI | MR | Zbl

[6] A. T. Sazonova, “O resheniyakh odnogo klassa sistem nelineinykh differentsialnykh uravnenii, svyazannogo s zadachei chetyrekh tel”, Vesnik GrDU. Seryya 2. Matematyka. Fizika. Infarmatyka, vylichalnaya tekhnika i kiravanne, 2013, no. 3(159), 56–60 | MR

[7] A. T. Sazonova, “O resheniyakh odnoi uproschennoi sistemy nelineinykh differentsialnykh uravnenii, svyazannoi s zadachei chetyrekh tel”, Problemy fiziki, matematiki, tekhniki, 2014, no. 1(18), 69–73

[8] A. T. Sazonova, “O nekotorykh sluchayakh razreshimosti uproschennykh sistem v zadache dvizheniya chetyrekh tel pod deistviem sil gravitatsii”, Vesnik GrDU. Seryya 2. Matematyka. Fizika. Infarmatyka, vylichalnaya tekhnika i kiravanne, 2014, no. 1(170), 42–52

[9] I. P. Martynov, N. S. Berezkina, V. A. Pronko, Analiticheskaya teoriya nelineinykh uravnenii i sistem, posobie, GrGU, Grodno, 2009, 395 pp.

[10] A. T. Lozovskaya, “O resheniyakh odnogo klassa nelineinykh differentsialnykh uravnenii tretego poryadka, svyazannogo s zadachei trekh tel”, Nauka-2008, Sb. nauch. st. aspirantov i magistrantov GrGU im. Ya. Kupaly, eds. A. F. Pronevich i dr., Grodno, 2008, 294–301