The article is devoted to theoretical approaches to the use of differential matrix systems for calculating the aerodynamic maneuver of satellites. The algorithm for changing the inclination of the orbital plane and the longitude of the ascending node is presented. The authors analyzed the curvature of the descent trajectory in the atmosphere to change the longitudinal and lateral descent range, taking into account the expansion of the entrance corridor. Parameters of variation of the orbital phase for phasing with another spacecraft are presented in differential matrix form, for example, when transporting a spacecraft to a meeting point with a space station. The differential matrix equation takes into account small changes in all the orbital elements for the transition to a new given orbit or for the correction of the original orbit. A priori, several of the required combinations of altitude and flight speed were selected for optimal control, the corresponding values of the parameters of the space environment in front of the satellite are determined. The parameters of the evolution of the orbits are analytically presented, which make it possible to find regions of stability on the plane of the parameters of the major semiaxis and inclination for different quantities. In this paper, the authors show analytically that the use of trajectories of a multipulse transition to high circular orbits of satellites with large inclinations increases the final mass of the satellite, and also allows the satellite to be brought to final orbits with given distance values at the point of application of the intermediate pulse.

1.
Balducci
,
A.
,
Boelens
,
L.
,
Hillier
,
J.
,
Nyseth
,
T.
, &
Wilkinson
,
C.
(
2011
).
Introduction: Strategic spatial planning in uncertainty: theory and exploratory practice
.
Town Planning Review
,
82
(
5
),
481
501
.
2.
Wu
,
C. J.
, &
Hamada
,
M. S.
(
2011
).
Experiments: planning, analysis, and optimization
(Vol.
552
).
John Wiley & Sons
.
3.
Makridenko
L.A.
,
Gecha
V.Ya.
,
Sidnyaev
N.I.
,
Onufriev
V.V.
,
Govor
S.A.
(
2017
).
Determination of the height characteristics of electric rocket engines of a spacecraft using experiment-planning methods
.
Management problems.
(
1
).
4.
Kéchichian
,
J. A.
(
2018
). Applied Nonsingular Astrodynamics: Optimal Low-Thrust Orbit Transfer (Vol.
45
).
Cambridge University Press
.
5.
Tschauner
,
J.
, &
Hempel
,
P.
(
1965
).
Rendezvous with a target in an elliptical orbit
.
Astronautica Acta
,
11
(
2
),
104
109
.
6.
Billik
,
B. H.
(
1964
).
Some optimal low-acceleration rendezvous maneuvers
.
AIAA journal
,
2
(
3
),
510
516
.
7.
Lange
,
B. O.
(
1964
).
The control and use of drag-free satellites
.
Dept. of Electrical Engineering
.
8.
Lange
,
B. O.
, &
Smith
,
R. G.
(
1965
).
The application of Floquet theory to the computation of small orbital perturbations over long time intervals using the Tschauner-Hempel equations
.
9.
Lange
,
B. O.
, &
Parkinson
,
B. W.
(
1966
). Error Equations of Inertial Navigation with Special Application to Orbital Determination and Guidance. In
Progress in Astronautics and Rocketry
(Vol.
17
, pp.
209
246
).
Elsevier
.
10.
Battin
,
R. H.
(
1964
).
Astronautical guidance (Book on astronautical guidance covering celestial mechanics and navigation, two-body orbital transfer, perturbation methods and guidance theory)
.
NEW YORK
,
MCGRAW-HILL BOOK CO.
, 1964.
400
P.
11.
Pease
,
M. C.
(
1965
).
Methods of matrix algebra (No. 512.896 P43
).
12.
Pease
,
M. C.
(
1965
).
Formalization of the Lagrangian, the Hamiltonian, and Related Concepts
.
Journal of Mathematical Physics
,
6
(
10
),
1558
1563
.
13.
Synge
,
J. L.
,
Truesdell
,
C. A.
, &
Toupin
,
R. A.
(
1960
).
HandbuchderPhysik
.
14.
Sanz-André
,
N.
, s,
Juli-Uuml
,
Santiago-Prowald
,
N.
, &
Ayuso-Barea
,
A.
(
1997
).
Spacecraft launch depressurization loads
.
Journal of spacecraft and rockets
,
34
(
6
),
805
810
.
15.
Ivanov
,
N. M.
,
Dmitrievskii
,
A. A.
, &
Lysenko
,
L. N.
(
1986
). Spacecraft ballistics and navigation.
Moscow Izdatel Mashinostroenie
.
16.
Akin
,
D.
(
1990
).
The Parashield Entry Vehicle Concept: Basic Theory and Flight Test Development
.
17.
Alfriend
,
K.
,
Vadali
,
S. R.
,
Gurfil
,
P.
,
How
,
J.
, &
Breger
,
L.
(
2009
). Spacecraft formation flying: Dynamics, control and navigation (Vol.
2
).
Elsevier
.
18.
Novykov
,
O.
,
Tikhonov
,
V.
, &
Litvinov
,
V.
(
2016
).
Methods of Analysis for Launch Vehicle Injection Accuracy/Methods for analyzing the accurancy of launch vehicles
.
19.
Ivanov
N.M.
,
Lysenko
L.N.
(
2004
).
Ballistics and navigation spacecraft. LLC
DROFA
”.
20.
Razorenov
G.N.
,
Bakhramov
E.A.
,
Titov
Yu.F.
(
2003
).
Aircraft control system (ballistic missiles and their warheads
).
M.: Engineering.
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