Search

Use of Dynamical Pfaff‘s Eq uations in the Lie Transformations // Tomsk State Pedagogical University Bulletin. 2011. Issue 5 (107). P. 11-17

In the present paper the connection of Pfaff’s equations with Lie transformations is considered. The averaging method in the restricted three-body problem based on Lie transformations in Pfaff’s space is proposed. The efficiency of such an algorithm for the problem of asymptotic integration in dynamics is discussed for the case where the solutions of the problem require a great number of approximations.

Keywords: perturbation theory, averaging method, Lie transformations, Pfaff’s equations, restricted three-body problem, satellites dynamics.

THE USE OF MODIFIED HILL’S VARIABLES IN THE METHOD OF AVERAGING // Tomsk State Pedagogical University Bulletin. 2011. Issue 8 (110). P. 53-56

In this paper the modified Hill’s canonical variables are introduced. They are v, G, H; r, g, h, where r is the distance to the primary for Keplerian orbit ; v = dr / dt; G= aј(1e2) and H = G cos i are Delaunay’s variables; g = Й is the argument of the periapsis; h = © is the longitude of the ascending node. We show that the modified Hill’s canonical variables are useful in some analytical theories of motion where it is need to avoid expansion of the perturbations in powers of eccentricity and where it is advantageous to use the eccentric anomaly as independent variable. As an example, we consider the single-averaged analytical model in the frame of the restricted three-body problem for satellite case.

Keywords: небесная механика, теория возмущений, метод усреднения, преобразования Ли, канонические переменные Хилла, ограниченная задача трех тел, динамика спутников планет

POST-NEWTONIAN EFFECTS IN THE MOTION OF THE INNERMOST JUPITER’S SATELLITES // Tomsk State Pedagogical University Bulletin. 2012. Issue 7 (122). P. 70-75

In the present paper the possibility of measuring general relativistic effects on the orbits of the inner Jupiter’s satellites are discussed. We consider for Amalthea J5 the question if the PN components of orbital precession can be isolated from the far larger Newtonian precession. The results of several numerical simulations have shown that all larger contributions of Newtonian perturbations can be modeled and subtracted out.

Keywords: celestial mechanics, perturbation theory, satellites dynamics, relativistic effects, Jupiter’s satellites

POST-NEWTONIAN EFFECTS IN THE MOTION OF THE NEAREST SATELLITES OF JUPITER // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 39-41

In this article the possibility of measurement of post-Newtonian effects in the motion of close satellites of Jupiter is discussed. On an example of Jupiter's fth satellite Amalthea we study a question of, whether can be isolated the PN component of orbital precession of the satellite from much bigger Newtonian components. Results of researches have shown that all larger contributions of Newtonian perturbations can be modeled and subtracted out.

Keywords: celestial mechanics, perturbation theory, satellites dynamics, relativistic effects, Jupiter's satellites

ANALYTICAL PROPER ELEMENTS FOR THE SATELLITE SYSTEMS // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 22-24

In this paper, we present the theoretical basis of the calculation of proper elements for the irregular satellites of the giant planets. We use the averaging method for solving the restricted three-body problem. This method is based on applying transformations Lie in the space of Pfaff. Expressions for the short-period perturbations are obtained in the form of series in powers of the small parameter  (the ratio of the mean motions of the Sun and satellite) and in a closed form relative eccentricities and inclinations. This is important, as the specific application objects have orbits with large values of these parameters.

Keywords: proper elements, Lie transformation, Pfaff’s space, irregular satellites