Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
The Research of Motion in a Neighborhood of Collinear Libration Point by Conservative Methods. / Shmyrov, A.; Shmyrov, V.; Shymanchuk, D.
Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017. ed. / MD Todorov. Vol. 1895 American Institute of Physics, 2017. 060003 (AIP Conference Proceedings; Vol. 1895).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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TY - GEN
T1 - The Research of Motion in a Neighborhood of Collinear Libration Point by Conservative Methods
AU - Shmyrov, A.
AU - Shmyrov, V.
AU - Shymanchuk, D.
PY - 2017
Y1 - 2017
N2 - In this paper we research the orbital motion described by equations in hamiltonian form. The shift mapping along a trajectory of motion is canonical one and it makes possible to apply conservative methods. The examples of application of such methods in problems of celestial mechanics are given. The first order approximation of generating function of shift mapping along the trajectory is constructed for uncontrolled motion in a neighborhood of collinear libration point of Sun-Earth system. Also this approach is applied to controllable motion with special kind of control, which ensuring the preservation of hamiltonian form of the equations of motion. The form of iterative schemes for numerical modeling of motion is given. For fixed number of iterations the accuracy of presented numerical method is estimated in comparison with Runge-Kutta method of the fourth order. The analytical representation of the generating function up to second-order terms with respect to time increment is given.
AB - In this paper we research the orbital motion described by equations in hamiltonian form. The shift mapping along a trajectory of motion is canonical one and it makes possible to apply conservative methods. The examples of application of such methods in problems of celestial mechanics are given. The first order approximation of generating function of shift mapping along the trajectory is constructed for uncontrolled motion in a neighborhood of collinear libration point of Sun-Earth system. Also this approach is applied to controllable motion with special kind of control, which ensuring the preservation of hamiltonian form of the equations of motion. The form of iterative schemes for numerical modeling of motion is given. For fixed number of iterations the accuracy of presented numerical method is estimated in comparison with Runge-Kutta method of the fourth order. The analytical representation of the generating function up to second-order terms with respect to time increment is given.
UR - http://www.scopus.com/inward/record.url?scp=85031673800&partnerID=8YFLogxK
U2 - 10.1063/1.5007388
DO - 10.1063/1.5007388
M3 - статья в сборнике материалов конференции
AN - SCOPUS:85031673800
VL - 1895
T3 - AIP Conference Proceedings
BT - Application of Mathematics in Technical and Natural Sciences
A2 - Todorov, MD
PB - American Institute of Physics
Y2 - 21 June 2017 through 26 June 2017
ER -
ID: 9180673