Keywords cloud
Taking into account this pro vision and some other assumptions, the procedures have been determined for simultaneous application of the Euler equation and its analogue being non-invariant in relation to the coordinate system. Key words: first variation of a functional , joint application of extremality conditions , non-invariance in relation to the coordinate system , parametric shape of the second variation , optimum curves of descent Bibliography: 1. first variation of a functional , joint application of extremality conditions , non-invariance in relation to the coordinate system , parametric shape of the second variation , optimum curves of descent .
]]>1. Solving a problem of optimum curves of descent using the enhanced Euler equation
Organization:
Yangel Yuzhnoye State Design Office, Dnipro, Ukraine1; The National Academy of Sciences of Ukraine, Kyiv, Ukraine2
Page: Kosm. teh. Raket. vooruž. 2020, (1); 3-12
DOI: https://doi.org/10.33136/stma2020.01.003
Language: Russian
Annotation: The purpose of this study is the enhancement of Euler equation possibilities in order to solve the brachistochrone problem that is the determination of a curve of fastest descent. There are two circumstances: 1) the first integral of an Euler equation does not contain a partial derivative of integrand with respect to y in an explicit form; 2) when the classical Euler equation is derived, only the second term of integrand is integrated by parts. This allowed formulating a problem of determination of new conditions of functional extremality. It is assumed that the integrand of the first variation of a functional is equal to zero. Taking into account this pro vision and some other assumptions, the procedures have been determined for simultaneous application of the Euler equation and its analogue being non-invariant in relation to the coordinate system. The brachistochrone problem was solved using these equations: the curves that satisfy the conditions of weak minimum optimality were plotted. The time of a material point’s descent along the suggested curves and the classic extremals was numerically compared. It is shown that the application of suggested curves ensures short descent time as compared to the classic extremals.
Key words: first variation of a functional, joint application of extremality conditions, non-invariance in relation to the coordinate system, parametric shape of the second variation, optimum curves of descent
Bibliography:
1. Bliss G. A. Lektsii po variatsionnomu ischisleniiu. М., 1960. 462 s.
2. Yang L. Lektsii po variatsionnomu ischisleniiu i teorii optimalnogo uravneniia. М.,1974. 488 s.
3. Elsgolts L. E. Differentsialnye uravneniia i variatsionnoe ischislenie. М., 1965. 420 s.
4. Teoriia optimalnykh aerodinamicheskikh form / pod red. А. Miele. М., 1969. 507 s.
5. Shekhovtsov V. S. O minimalnom aerodinamicheskom soprotivlenii tela vrashcheniia pri nulevom ugle ataki v giperzvukovom neviazkom potoke. Kosmicheskaia tekhnika. Raketnoe vooruzhenie: Sb. nauch.-tekhn. st. / GP “KB “Yuzhnoye”. Dnipro, 2016. Vyp. 2. S. 3–8.
6. Sumbatov А. S. Zadacha o brakhistokhrone (klassifikatsiia obobshchenii i nekotorye poslednie resultaty). Trudy MFTI. 2017. T. 9, №3 (35). S. 66–75.
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This data is used to determine the rocket’s reference attitude (orientation of object-centered coordinates in the geographical reference system) in the steady mode.
]]>10. Method of autonomous determination of the rocket’s reference attitude during pre-launch processing
Organization:
Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
Page: Kosm. teh. Raket. vooruž. 2024, (1); 85-92
DOI: https://doi.org/10.33136/stma2024.01.085
Language: Ukrainian
Annotation: To solve the navigation tasks (determination of the apparent accelerations and angular velocities and calculation of rocket orientation angles) in the rocket engineering, the data from the sensing elements (angular velocity sensors and accelerometers) is used. Accuracy of reference attitude determination of the rocket in the steady mode (at lift-off) has great influence on accuracy of the received navigation data during the flight. Gimballess inertial navigation system, built on the basis of inertial MEMS-sensors of Industry class (three angular velocity sensors and three accelerometers), is taken as the navigation device. In the classical version, the integration of data from angular velocity sensors and from accelerometers is the basis of gimballess inertial navigation system operation. It results in accumulation of errors when solving the navigation task (in particular due to the integration of data from angular velocity sensors). Taking it into consideration, the alternative method of rocket’s reference attitude determination during the pre-launch processing is offered. This method does not use mathematical operations of integration and is autonomous. Initial data, received from the gimballess inertial navigation system, is used as the output data. This data is used to determine the rocket’s reference attitude (orientation of object-centered coordinates in the geographical reference system) in the steady mode. Orientation angles are determined without the integration of data picked up from the angular velocity sensors. The comparative analysis to define the processing efficiency of the navigation device initial data was held during the determination of the rocket’s orientation angles in the steady mode, using the proposed method and Runge-Kutta method. The received results showed that accuracy of the reference attitude determination with the proposed method is higher. Thus, the proposed method will help reduce the errors in determination of the rocket’s reference attitude in the steady mode that in the future will improve the accuracy in determination of navigational parameters during the rocket’s flight.
Key words: navigation system, mems-sensors, accelerometers, angular velocity sensors, reference attitude
Bibliography:
- Meleshko V.V., Nesterenko O.I. Besplatformennye inertsialnye navigatsionnye systemy. Ucheb. posobie. Kirovograd: POLIMED – Service, 2011. 164 s.
- Vlasik S.N., Gerasimov S.V., Zhuravlyov A.A. Matematicheskaya model besplatformennoy inertsialnoy navigatsionnoy systemy i apparatury potrebitelya sputnikovoi navigatsionnoy systemy aeroballisticheskogo apparata. Nauka i technika Povitryannykh Sil Zbroinykh Sil Ukrainy. 2013. № 2(11). s. 166-169.
- Waldenmayer G.G. Protsedura pochatkovoi vystavki besplatformennoy inertsialnoy navigatsionoy systemy z vykorystannyam magnitometra ta rozshirennogo filtra Kalmana. Aeronavigatsini systemy. 2012. s. 8.
- Korolyov V.M., Luchuk Ye.V., Zaets Ya.G., Korolyova O.I., Miroshnichenko Yu.V. Analiz svitovykh tendentsiy rozvytku system navigatsii dlya sukhoputnykh viysk. Rozroblennya ta modernizatsia OVT. 2011. №1(4). s.19-29. https://doi.org/10.33577/2312-4458.4.2011.19-29
- Avrutov V.V., Ryzhkov L.M. Pro alternativniy metod avtonomnogo vyznachennya shyroty i dovgoty rukhomykh obiektiv. Mekhanika gyroskopichnykh system. 2021. №41. s. 122-131. https://doi.org/10.20535/0203-3771412021269255
- Bugayov D.V., Avrutov V.V., Nesterenko O.I. Experimentalne porivnyannya algoritmiv vyznachennya orientatsii na bazi complimentarnogo filtru ta filtru Madjvika. Avtomatizatsiya technologichnykh i biznes-protsesiv. 2020. T. 12, №3. s. 10-19.
- Chernyak M.G., Kolesnik V.O. Zmenshennya chasovykh pokhibok inertsialnogo vymiryuvalnogo modulya shlyakhom realizatsii yogo strukturnoi nadlyshkovosti na bazi tryvisnykh micromekhanichnykh vymiruvachiv. Mekhanika giroskopichnykh system. 2020. №39. s. 66-80. https://doi.org/10.20535/0203-3771392020229096
- Rudik A.V. Matematichna model pokhibok accelerometriv bezplatformenoi inertsialnoi navigatsinoi systemy. Visnyk Vynnitskogo politechnychnogo institutu. 2017. №2. s. 7-13.
- Naiko D.A., Shevchuk O.F. Teoriya iomovirnostey ta matematychna statistika: navch. posib. Vinnytsya: VNAU. 2020. 382 s.
- Matveev V.V., Raspopov V.Ya. Osnovy postroeniya bezplatformennykh inertsialnykh navigatsionnykh system. SPb.: GNTs RF OAO «Kontsern «TsNII «Electropribor». 2009. 280 s.
- Novatorskiy M.A. Algoritmy ta metody obchislen’ [Electronniy resurs]: navch. posib. dlya stud. KPI im. Igorya Sikorskogo. Kiyv: KPI im. Igorya Sikorskogo. 2019. 407 s.
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Keywords cloud
Taking into account the difficulties of writing the analytical expressions for these figures during the transition to the launch coordinate system and further integration when identifying the risk, in practical calculations we propose to approximate the zone of dangerous impact of the failed LV/ILV using a polygon.
]]>5. Assessment of risk of toxic damage to people in case of a launch vehicle accident at flight
Organization:
Page: Kosm. teh. Raket. vooruž. 2024, (1); 40-50
DOI: https://doi.org/10.33136/stma2024.01.040
Language: English
Annotation: Despite stringent environmental requirements, modern launch vehicles/integrated launch vehicles (LV/ILV)
burn toxic propellants such as NTO and UDMH. Typically, such propellants are used in the LV/ILV upper
stages, where a small amount of propellant is contained; however, some LV/ILV still use such fuel in all
sustainer propulsion stages. For launch vehicles containing toxic rocket propellants, flight accidents may result
in the failed launch vehicle falling to the Earth’s surface, forming large zones of chemical damage to people
(the zones may exceed blast and fire zones). This is typical for accidents occurring in the first stage flight
segment, when an intact launch vehicle or its components (usually individual stages) with rocket propellants
will reach the Earth’s surface. An explosion and fire following such an impact will most likely lead to a massive
release of toxicant and contamination of the surface air. An accident during the flight segment of the LV/ILV
first stage with toxic rocket propellants, equipped with a flight termination system that implements emergency
engine shutdown in case of detection of an emergency situation, has been considered. To assess the risk
of toxic damage to a person located at a certain point, it is necessary to mathematically describe the zone
within which a potential impact of the failed LV/ILV will entail toxic damage to the person (the so-called zone
of dangerous impact of the failed LV/ILV). The complexity of this lies in the need to take into account the
characteristics of the atmosphere, primarily the wind. Using the zone of toxic damage to people during the fall
of the failed launch vehicle, which is proposed to be represented by a combination of two figures: a semicircle
and a half-ellipse, the corresponding zone of dangerous impact of the failed LV/ILV is constructed. Taking into
account the difficulties of writing the analytical expressions for these figures during the transition to the launch
coordinate system and further integration when identifying the risk, in practical calculations we propose to
approximate the zone of dangerous impact of the failed LV/ILV using a polygon. This allows using a known
procedure to identify risks. A generalization of the developed model for identifying the risk of toxic damage
to people involves taking into account various types of critical failures that can lead to the fall of the failed
LV/ILV, and blocking emergency engine shutdown during the initial flight phase. A zone dangerous for people
was constructed using the proposed model for the case of the failure of the Dnepr launch vehicle, where the
risks of toxic damage exceed the permissible level (10–6). The resulting danger zone significantly exceeds the
danger zone caused by the damaging effect of the blast wave. Directions for further improvement of the model
are shown, related to taking into account the real distribution of the toxicant in the atmosphere and a person’s
exposure to a certain toxic dose.
Key words: launch vehicle, critical failure, flight accident, zone of toxic damage to people, zone of dangerous impact of the failed launch vehicle, risk of toxic damage to people.
Bibliography:
- Hladkiy E. H. Protsedura otsenky poletnoy bezopasnosti raket-nositeley, ispolzuyuschaya geometricheskoe predstavlenie zony porazheniya obiekta v vide mnogougolnika. Kosmicheskaya technika. Raketnoe vooruzhenie: sb. nauch.-techn. st. Dnepropetrovsk: GP «KB «Yuzhnoye», 2015. Vyp. 3. S. 50 – 56. [Hladkyi E. Procedure for evaluation of flight safety of launch vehicles, which uses geometric representation of object lesion zone in the form of a polygon. Space Technology. Missile Weapons: Digest of Scientific Technical Papers. Dnipro: Yuzhnoye SDO, 2015. Issue 3. Р. 50 – 56. (in Russian)].
- Hladkiy E. H., Perlik V. I. Vybor interval vremeni blokirovki avariynogo vyklucheniya dvigatelya na nachalnom uchastke poleta pervoy stupeni. Kosmicheskaya technika. Raketnoe vooruzhenie: sb. nauch.-tech. st. Dnepropetrovsk: GP «KB «Yuzhnoye», 2011. Vyp. 2. s. 266 – 280. [Hladkyi E., Perlik V. Selection of time interval for blocking of emergency engine cut off in the initial flight leg of first stage. Space Technology. Missile Weapons: Digest of Scientific Technical Papers. Dnipro: Yuzhnoye SDO, 2011. Issue 2. Р. 266 – 280. (in Russian)].
- Hladkiy E. H., Perlik V. I. Matematicheskie modeli otsenki riska dlya nazemnykh obiektov pri puskakh raket-nositeley. Kosmicheskaya technika. Raketnoe vooruzhenie: sb. nauch.-techn. st. Dnepropetrovsk: GP «KB «Yuzhnoye», 2010. Vyp. 2. S. 3 – 19. [Hladkyi E., Perlik V. Mathematic models for evaluation of risk for ground objects during launches of launch-vehicles. Space Technology. Missile Weapons: Digest of Scientific Technical Papers. Dnipro: Yuzhnoye SDO, 2010. Issue 2. P. 3 – 19. (in Russian)].
- NPAOP 0.00-1.66-13. Pravila bezpeki pid chas povodzhennya z vybukhovymy materialamy promyslovogo pryznachennya. Nabrav chynnosti 13.08.2013. 184 s [Safety rules for handling explosive substances for industrial purposes. Consummated 13.08.2013. 184 p.
(in Ukranian)]. - AFSCPMAN 91-710 RangeSafetyUserRequirements. Vol. 1. 2016 [Internet resource]. Link : http://static.e-publishing.af.mil/production/1/afspc/publicating/
afspcman91-710v1/afspcman91-710. V. 1. pdf. - 14 CFR. Chapter III. Commercial space transportation, Federal aviation administration, Department of transportation, Subchapter C – Licensing, part 417 – Launch Safety, 2023 [Internet resource]. Link: http://law.cornell.edu/cfr/text/14/part-417.
- 14 CFR. Chapter III. Commercial space transportation, Federal aviation administration, Department of transportation, Subchapter C – Licensing, part 420 License to Operate a Launch Site. 2022 [Internet resource]. Link: http://law.cornell.edu/cfr/text/14/part-420.
- ISO 14620-1:2018 Space systems – Safety requirements. Part 1: System safety.
- 9 GOST 12.1.005-88. Systema standartov bezopasnosti truda. Obschie sanitarno-gigienicheskie trebovaniya k vozdukhu rabochei zony. [GOST 12.1.005-88. Labor safety standards system. General sanitary and hygienic requirements to air of working zone].
- 10 Rukovodyaschiy material po likvidatsii avarijnykh bolshykh prolivov okislitelya АТ (АК) i goruchego NDMG. L.:GIPKh, 1981, 172 s. [Guidelines on elimination of large spillages of oxidizer NTO and fuel UDMH. L.:GIPH, 1981, 172 p. (in Russian)].
- 11 Kolichestvennaya otsenka riska chimicheskykh avariy. Kolodkin V. M., Murin A. V., Petrov A. K., Gorskiy V. G. Pod red. Kolodkina V. M. Izhevsk: Izdatelskiy dom «Udmurtskiy universitet», 2001. 228 s. [Quantitative risk assessment of accident at chemical plant. Kolodkin V., Murin A., Petrov A., Gorskiy V. Edited by Kolodkin V. Izhevsk: Udmurtsk’s University. Publish house, 2001. 228 p. (in Russian)].
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Keywords cloud
The new condition of extremeness unlike Euler equation is noninvariant relative to coordinate system. Key words: the first variation of functional , combined usage of conditions of extremeness , noninvariance relative to coordinate system , parametrical form of the second variation , optimal curves of descent Bibliography: 1 Shekhovtsov V. the first variation of functional , combined usage of conditions of extremeness , noninvariance relative to coordinate system , parametrical form of the second variation , optimal curves of descent .
]]>13. On an Approach to Constructing the Extremes in the Tasks of Optimal Solutions Search
Organization:
Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
Page: Kosm. teh. Raket. vooruž. 2018 (2); 117-126
DOI: https://doi.org/10.33136/stma2018.02.117
Language: Russian
Annotation: The purpose of the article is development of a modified variational method to determine extremals in the tasks of search for optimal solutions. The method has been developed using the results of investigations of the first variation of functional with autonomous subintegral function for the problem with fixed ends. The assumption of non-zero values of variation of function at boundary points has been introduced. It is shown that when using this assumption and introducing some other assumptions and limitations, it is possible to expand the class of permissible functions, among which the extremal curves should be sought for. With this expansion, to construct one extremal it is necessary to use two conditions of extremeness, one of which is Euler equation. To fulfill them, it is necessary to realize the constancy of partial derivative from subintegral function of desired variable at each point of interval considered. The new condition of extremeness unlike Euler equation is noninvariant relative to coordinate system. The use of this property allows, at presentation of the second variation of functional in parametrical form, constructing the solutions that satisfy the necessary and sufficient conditions of local minimum (maximum). It is noted that the proposed method is the first step in the development of a new approach to solution of multidimensional variational problems. The use of the latter will allow obtaining new solutions of various problems of technical mechanics, such as the task of determining optimal trajectory parameters of launch vehicles in the phase of designing and development of technical proposals, selection of optimal flight modes et al. The efficiency of the proposed method is demonstrated by example of solving the known problem about brachistichrone – determination of the curve of quickest descent. Using the method, two curves have been constructed that satisfy the necessary and sufficient conditions of optimality. The results are presented of comparison of time of material point descent along the proposed curves and descent along classical extremals. It is shown that the time of descent along the proposed curves is shorter than that at descent along classical exteremals.
Key words: the first variation of functional, combined usage of conditions of extremeness, noninvariance relative to coordinate system, parametrical form of the second variation, optimal curves of descent
Bibliography:
1 Shekhovtsov V. S. On Minimal Aerodynamic Resistance of Rotation Body at Zero Attack Angle in Hypersonic Frictionless Flow. Space Technology. Missile Armaments: Collection of scientific-technical articles. 2016. Issue 2. P. 3-8.
2. Theory of Optimal Aerodynamic Shapes / Under the editorship of A. Miele. М., 1969. 507 p.
3. Sumbatov A. S. Least-Time Flight Path Problem (classification of generalizations and some latest results). Works of MFTI. 2017. Vol. 9, No. 3 (35). P. 66-75.
4. Bliss G. A. Lectures on Variational Calculus. М., 1960. 462 p.
5. Yang L. Lectures on Variational Calculus and Optimal Control Theory. М., 1974. 488 p.
6. Elsgolts L. E. Differential Equations and Variational Calculus. М., 1965. 420 p.
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Keywords cloud
2019, (1); 81-86 DOI: https://doi.org/10.33136/stma2019.01.082 Language: Russian Annotation: Under the Sea Launch program when developer of the Zenit-3SL ILV control system issued the permission to launch in the conditions of drift from the design launch point of the Odyssey launch platform, the problem of drift parameters monitoring at the Sea Launch Commander ACS appeared. Geographical coordinates – latitude and longitude of the platform according to the GPS sensor, installed on the platform are used for calculations.
]]>12. Monitoring of Launch Platform Drift Parameters during Zenit-3SL Integrated Launch Vehicle Prelauch Processing
Organization:
Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
Page: Kosm. teh. Raket. vooruž. 2019, (1); 81-86
DOI: https://doi.org/10.33136/stma2019.01.082
Language: Russian
Annotation: Under the Sea Launch program when developer of the Zenit-3SL ILV control system issued the permission to launch in the conditions of drift from the design launch point of the Odyssey launch platform, the problem of drift parameters monitoring at the Sea Launch Commander ACS appeared. To ensure the payload orbiting accuracy the following maximum permissible values of platform drift parametres were determined:
• maximum velocity of platform drift – no more than 0,32 m/s;
• maximum acceleration of platform drift – no more than ±0,05 m/s2;
• maximum distance of platform drift from design launch point – no more than 1950 m.
The article includes the computation algorithm of the platform drift parametres to calculate velocity and acceleration of the drift, as well as distance from the design launch point to the actual point of the platform location. Geographical coordinates – latitude and longitude of the platform according to the GPS sensor, installed on the platform are used for calculations. These values during prelaunch processing of the ILV are transmitted to the assembly and command ship’s workstation for calculation of loads in the ILV root section at the rate of once in a second. During one of the Sea Launch missions, C++ program was developed and installed on the loads calculation workstation, realizing the computation algorithm offered by the authors of this article. This program displayed in real time the monitored parametres of the platform drift, and monitored the tolerable limits. During the same mission, the correctness of the developed algorithm and program were confirmed during the special experiment on the launch platform drift in the launch point. In future, they were used during the subsequent missions of the Sea Launch program.
Key words: Sea Launch, latitude, longitude, algorithm, velocity, acceleration
Bibliography:
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Keywords cloud
Then the coordinates of machine tool are determined. For this purpose, we determine the angles of coil winding, corresponding angles of mandrel turn in determined coordinates X, the coordinates of band escape point, angle of inclination of free section of band, then from geometrical considerations we obtain the components of unit vector of tangent to reinforcing trajectory and directly the coordinated of machine tool actuators. Using the presented logics, similarly it is easy to obtain for all coils the coordinates of machine tool actuators. According to this technique, the Vitok auto-programming system was developed in MathCad environment. The Vitok system was used during development of winding program for tube 28x28x2 mm under Sich-2M program.
]]>11. Winding the tubes of rectangular section using dowels
Organization:
Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
Page: Kosm. teh. Raket. vooruž. 2019, (2); 80-91
DOI: https://doi.org/10.33136/stma2019.02.080
Language: Russian
Annotation: The tubes of rectangular section made of composite material find ever- growing use. Winding of tubes without using dowels for small winding angles has a number of disadvantages. The technology of winding through dowels does not have these disadvantages. The paper presents the authors-developed calculation technique for programs of winding the tubes of rectangular section made of composite materials using dowels. To ensure winding continuity, the dowels at base must have equal distances between them. The external diameter of comb is selected with margin taking into account band stranding on the dowels. The scheme of winding on entire layer is determined that represents a table which indicates band position between the dowels of front and rear comb during winding a layer for each coil. Then the coordinates of machine tool are determined. For this purpose, we determine the angles of coil winding, corresponding angles of mandrel turn in determined coordinates X, the coordinates of band escape point, angle of inclination of free section of band, then from geometrical considerations we obtain the components of unit vector of tangent to reinforcing trajectory and directly the coordinated of machine tool actuators. As a result, we obtain the table of coordinates of machine toll actuators during winding of the first coil (at forward and back travel). Using the presented logics, similarly it is easy to obtain for all coils the coordinates of machine tool actuators. According to this technique, the Vitok auto-programming system was developed in MathCad environment. The Vitok system was used during development of winding program for tube 28x28x2 mm under Sich-2M program. The programs operated successfully. The test samples of tubes were wound. The authors performed winding of the tubes of rectangular section made of composite material to obtain a structure with zero linear thermal expansion coefficient.
Key words: reinforcing trajectory, laying roller, comb, winding scheme, winding angle, coordinates of machine tool actuators
Bibliography:
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To tilt the spacecraft uses reaction wheels, installed in axes of coordinate system coupled with spacecraft center of mass. Simulation initial con-ditions correspond to the attitude control mode of the spacecraft relative to the orbital coordinate system with the specified accuracy. Key words: electrical axis of the antenna , mathematical model , coordinate system , transformation matrix , vector Bibliography: 1. electrical axis of the antenna , mathematical model , coordinate system , transformation matrix , vector .
]]>4. On control of spacecraft orientation to the ground data acquisition station
Organization:
Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
Page: Kosm. teh. Raket. vooruž. 2023 (1); 41-47
DOI: https://doi.org/10.33136/stma2023.01.041
Language: English
Annotation: The article dwells on the spacecraft attitude control to point the onboard antenna to the ground data acquisition station during the communication session. Antenna is fixed relative to the spacecraft body. Pur-pose of the antenna is to receive the flight task aboard the spacecraft and to downlink the telemetry infor-mation. When orbiting, the spacecraft position relative to the ground data acquisition station changes contin-uously. It is due to the diurnal rotation of the Earth, spacecraft orbital motion and angular motion of the spacecraft relative to the center of mass under the impact of the disturbing and control moments. To tilt the spacecraft uses reaction wheels, installed in axes of coordinate system coupled with spacecraft center of mass. Electromagnets are used to unload the reaction wheels. The reaction wheels control law is suggested, which tilts the spacecraft to point the antenna to the ground data acquisition station. Mathematical model of the spacecraft dynamics relative to center of mass is given, using the suggested reaction wheels control law. The following external disturbing moments, acting on the spacecraft in flight, are taken into consideration: gravitational, magnetic, aerodynamic moments and solar radiation moment of forces. Dipole model of the magnetic field of the Earth is used to calculate the magnetic moments. Software was developed and space-craft dynamics was simulated on the personal computer with the specified initial data. Simulation initial con-ditions correspond to the attitude control mode of the spacecraft relative to the orbital coordinate system with the specified accuracy. Simulation results verify the applicability of the suggested reaction wheel control law.
Key words: electrical axis of the antenna, mathematical model, coordinate system, transformation matrix, vector
Bibliography:
1. Ivanova G.A., Ostapchuk S.V. Matematich-eskaya model magnitno-gravitatsionnoy sys-temy orientatsii dlya eksperimentalnogo mi-crosputnika. Kosmicheskaya technika. Raketnoye vooruzhennie: Nauch.-techn. sb. 2009. S. 192 -202.
2. Branets V.N., Shmyglevskiy I.P. Primenenie quoternionov v zadachah orientatsii tverdogo tela. M.: Nauka, 1973. 320 s.
3. Problemy orientatsii iskusstvennyh sputnikov Zemli. M.: Nauka, 1966. 350 s.
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