Магнитогидродинамические эффекты в задачах ориентации вращающихся космических аппаратов Борис Рабинович Институт Космических Исследований РАН Январь 2003

2 Аннотация Излагаются основные результаты теоретических и экспериментальных исследований, связанных с использованием магнитогидродинамических (МГД) эффектов в задачах стабилизации и ориентации вращающихся КА с деформируемыми элементами. Рассматривается новый принцип использования этих эффектов, основанный на идее «жидкого гироскопа» (вращающаяся тороидальная полость, частично заполненная электропроводной замагниченной жидкостью).

3 Предлагается использовать такого рода МГД- элементы для создания не требующих затрат рабочего тела, бесшарнирных систем ориентации и стабилизации вращающихся КА. МГД элементы новой конфигурации позволяют, в отличие от их первоначальной версии, реализовать постоянные и медленно меняющиеся управляющие моменты. При этом открываются широкие возможности включения в состав измерений не только интегрирующих акселерометров, но и солнечных датчиков

4 Автор благодарен ктн Алексею Гришину за большую работу по математическому моделированию и построению корневых годографов и кф-мн Виктории Прохоренко за подготовку электронной версии этого доклада

5 Stability of a rotating SC with a flexible element located along its rotation axis [1, 2]

6 Auroral Probe (INTERBALL project)

7 Mathematical model where

8 Stability condition where

9 Stability and instability domains for the rotating SC of the AP type: - - stability; + - instability (one unstable root); + + instability (two unstable roots) I

10 Root loci of the second and third roots for the variable parameters and I

11 Mathematical simulation of the nutation of the gyro-stable AP- type SC ( 0 = const = s -1 and c = 0.06 s -1 ): (a) s is a vector locus corresponding to the mass m displacement by the strains of the flexible element; (b) is a vector locus corresponding to the angular components of the SC s

12 Mathematical simulation of the nuta tion of the gyro-unstable SC of the AP type ( 0 = const = s -1 and c = 0.03 s -1 ): (a) s is a vector locus corresponding to the mass m displacement by the strains of the flexible element; (b) is a vector locus corresponding to the angular components of the SC s

13 MHD-element Theory and experiment [3, 4]

14 The MHD- element of the torus shape completely filled with an electroconductive magnetized liquid

15 Stability of a rotating SC with MHD-element in the control loop [5, 6]

16 Mathematical model of a rotating SC with MHD control The root of the characteristic equations responsible for the stability

17 Stabilization of the gyro-stable SC of the AP- type with MHD elements and accelerometers. The mathematical simulation for 0 = const = s -1, c = 0.06 s - 1 (a 0 = 2, a 1 = 3): (a) s is a vector locus corresponding to the mass m displacement by the strains of the flexible element; (b) is a vector locus corresponding to the angular components of the SC s

18 Stabilization of the gyro-unstable SC of the AP- type with MHD elements and accelerometers. The mathematical simulation for 0 = const = s -1, c = 0.03 s -1 (a 0 = 2, a 1 = 3): (a) s is a vector locus corresponding to the mass m displacement by the strains of the flexible element; (b) is a vector locus corresponding to the angular components of the SC s

19 Facility for the experimental studying of the MHD-phenomena 1, 2, 3 – the rotating MHD-element

20 Experimental results - Theory - Experiment without magnetic field - Experiment with magnetic field The hydrodynamical moment acting on the torus during the slow braking of its rotation Amplitude and phase responses of I/V control loop - Theory - Experiment, A(f) - Experiment, (f),

21 MHD-element for the attitude control and stabilization of a rotating spacecraft Some new ideas [7, 8, 9, 10]

22 Reminiscences concerning some problems of Rocket Carriers dynamics and stability The launches of N-1 heavy Rocket Carrier (RC) in the years 1969 – 1972 discovered the disturbing moment in the roll plane, caused by the twist of the Liquid Propellant Engines (LPE) jets combination around the longitudinal axis of the RC.

23 The heavy RC N-1 The view from the tail on the 30 LPE of the N-1 RC

24 The equilibrium forms of 8 interacting LPE jets a – The form with the regular symmetry b – The form with two planes of symmetry c - The form with screw symmetry

25 Mechanical models of the LPE jets forms presented in the previous slide a – The form with the regular symmetry b – The form with two planes of symmetry c - The form with the screw symmetry

26 The launch of N-1 RC 3-L

27 General comment to the slide 22 Analyzing the situation described above we see the arising in particular cases of the roll moment caused by a gas dynamical eccentricity of LPE jets. The moment is acting on a non rotating object (RC). We are looking forward to use the analogous phenomena for generating the pitch and yaw moments for the attitude control of the rotating SC. These moments must be in the contrary to the previous case under strict control. The point is that we can use for this purpose a hydro dynamical eccentricity with MHD control. Let us consider this problem more closely.

28 MHD effects in the Nature The forces acting on the elements of a rotating plasma torus Force lines of the Jovian magnetic field in the vicinity of the Io orbit Eccentric Jovian plasma torus including the Io moons orbit

29 Table 1. Parameters of Jupiter 1Radius R 0 [km] Period of self rotation T [hr]9. 9 3Gravitational acceleration on the planets equator g 0 [g] Strength of magnetic field on the planets equator μ 0 H 0 [Gauss] Eccentricity of dipole ε 0 [R 0 ] Inclination of dipole to the planets axis γ [deg] 9. 6

30 Table 2. Parameters of Jovian torus 1Radius r [R 0 ] MeanMinMax Mean eccentricity ε [r] Thickness h [r] MeanMinMax Mean strength of magnetic field μ 0 H [Gauss] Strength of magnetic field [μ 0 H] MeanMinMax

31 New MHD-element realizing the attitude control of a spinning SC Ferromagnetic magnet guide Electro conductive liquid Winding

32 Rotating SC with a new MHD-element Mathematical model Steady-state regime

33 MHD control of the three surface of the liquid

34 The fact of vital importance is that the system being under consideration has no hinges and does not need any special fuel expenses To confirm the new conception and to make the next step for its practical application we must fulfill a good deal of theoretical and experimental investigation.

35 References 1.Dokuchaev, L.V., Rabinovich, B.I. Analisis of Perturbed Motion near the Stability Boundary of a Rotating Spacecraft of the INTERBALL Auroral Probe Type, Cosmic Research, Vol. 37. No. 6, 1999, pp. 554 – Dokuchaev, L.V, Nazirov, R.R., Rabinovich, B.I., Ulyashin, A.I., On the Concordance of the Mathematical Model of Nutation of the Interball-2 Sattelite with a Flight Experiment. Cosmic Research, Vol. 38, No 5, 2000, pp. 454 – Rabinovich, B.I., Lebedev, V.G., Mytarev, A.I. Vortex Processes and Solid Body Dynamics. The Dynamic Problems of Spacecraft and Magnetic Levitation Systems. Kluwer Academic Publishers, Dordrecht, 1994, 296 p. 4.Churilov, G.A., Klishev, O.P., Mytarev, A.I., Rabinovich, B.I. Experimental Research of Toroidal Magnetohydrodynamic Element. Physical and Mathematical Models of Slow Breking Process, Scientific and technical journal «Polyot» («Flight»), No 9, 2001, pp. 21 – 27 (In Russian). 5.Dokuchaev, L.V., Rabinovich, B.I., Grishin, A.V. About the Stabilization of the Spacecraft with Deformable Elements Using the Magnetohydrodynamic Effects, Scientific and technical Journal «Polyot» («Flight»), No 7, 2000, pp. 21 – 27 (In Russian).

36 6. B.I. Rabinovich. Structural Control of a Rotating Spacecraft with Elastic Spike Antennas Using the Magnetohydrodynamic Control System. 3 rd International Workshop on Structural Control. Paris July 2000, pp Rabinovich, B.I., Prokhorenko., V.I. Concerning the rolling disturbance caused by the joint work of a Rocket Carriers LPR Engines, Preprint Space Research Institute Russian Academy of Sciences, Пр.-2023, 2000, Rabinovich, B.I. A Plasma Ring Rotating in a Gravitational.– Magnetic Field: The Stability Problem, Doklady Physics, Vol 44, No 7, 1999, pp. 482 – Rabinovich, B.I., Prokhorenko, V.I. A Spacecraft with a Liquid Stabilized by Rotation, Plasma Torus and Alfven`s Problem, Scientific and technical journal «Polyot» («Flight»), No 5, 1999, pp. 9 – 16 (In Russian). 10. B.I. Rabinovich. Some New Ideas of the Attitude Control Based on the Magnetohydrodynamic Phenomena. The Application to the Rotating Spacecraft. Astro2000, 11 CASI Conference on Astronautics, Ottawa, Canada, November 2000, p. 240a.