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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Steady-State Computation of Constant Rotational Rate Dynamic Stability Derivatives

Dynamic stability derivatives are essential to predicting the open and closed loop performance, stability, and controllability of aircraft. Computational determination of constant-rate dynamic stability derivatives (derivatives of aircraft forces and moments with respect to constant rotational rates) is currently performed indirectly with finite differencing of multiple time-accurate computational fluid dynamics solutions. Typical time-accurate solutions require excessive amounts of computational time to complete. Formulating Navier-Stokes (N-S) equations in a rotating noninertial reference frame and applying an automatic differentiation tool to the modified code has the potential for directly computing these derivatives with a single, much faster steady-state calculation. The ability to rapidly determine static and dynamic stability derivatives by computational methods can benefit multidisciplinary design methodologies and reduce dependency on wind tunnel measurements. The CFL3D thin-layer N-S computational fluid dynamics code was modified for this study to allow calculations on complex three-dimensional configurations with constant rotation rate components in all three axes. These CFL3D modifications also have direct application to rotorcraft and turbomachinery analyses. The modified CFL3D steady-state calculation is a new capability that showed excellent agreement with results calculated by a similar formulation. The application of automatic differentiation to CFL3D allows the static stability and body-axis rate derivatives to be calculated quickly and exactly.

Park, Michael A.↗
DOE OSTI2021

Dynamic P-Q Capability and Abnormal Operation Analysis of a Wind Turbine with Doubly-Fed Induction Generator

After several accidents occurred in wind farms in the United States and around the world, the subsynchronous oscillation (SSO) issues in grid-connected wind farms have gained serious attention. Particularly, these issues have caused significant challenges to wind turbines with a doubly fed induction generator (DFIG) because it is connected to the grid via both its stator and rotor paths. Traditionally, a P-Q capability chart is utilized to assure the safe operation boundary for a synchronous generator. But the energy conversion characteristics of a DFIG wind turbine are completely different. A critical factor to affect the reliable operation of a DFIG wind turbine is the rated current and pulse-width modulation (PWM) saturation constraints of its power converters. These constraint conditions can be affected by the wind turbine rotating speed and grid conditions. However, a detailed study of DFIG P-Q capability from these perspectives has not been conducted, which has hindered adequate understanding of many abnormal wind turbine operations reported in the literature and the development of advanced control technologies to overcome the challenges. The proposed study in this paper considers vector control implementation to DFIG power electronic converters in the dq reference frame, and the models and algorithms developed for the P-Q capability study have addressed specific DFIG power converter constraints that are different from those of a traditional synchronous generator. The paper especially focuses on exploring the dynamic natures of DFIG P-Q capability under uncertain and variable conditions to explore the root causes of many abnormal operations of DFIG wind turbines reported in the literature. The proposed study is validated through an electromagnetic transient simulation model of a grid-connected DFIG wind turbine. The proposed study has the potential to lead to the development of new DFIG control technologies that can help overcome the challenges for many abnormal operations of DFIG wind turbines.

17 WIND ENERGY↗
DOE OSTI2020

Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak

According to a recent paper [Hu et al ., Phys. Plasmas 26, 120702 (2019)], mode penetration at the top of the pedestal is a necessary and sufficient condition for the suppression of edge localized modes (ELMs) by a resonant magnetic perturbation (RMPs) in an H-mode tokamak discharge. This paper employs asymptotic matching theory to model a particular DIII-D discharge in which ELMs were suppressed by an externally generated, static, n ¼ 2, RMP whose amplitude was modulated at a frequency of 1 Hz. It is demonstrated that the response of the plasma to the applied RMP, in the immediate vicinities of the rational (i.e., resonant) surfaces, is governed by nonlinear, rather than by linear, physics. This is the case because the magnetic island widths associated with driven reconnection exceed the linear layer widths, even in cases where driven reconnection is strongly suppressed by plasma rotation. The natural frequency at a given rational surface (i.e., the helical frequency at which the locally resonant component of the RMP would need to propagate in order to maximize driven reconnection) is found to be offset from the local E B frame in the ion diamagnetic direction. The size of the offset is mostly determined by neoclassical poloidal rotation. Finally, the predictions of a fully nonlinear plasma response model are found to be broadly consistent with the DIII-D experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Incremental rotary rolling mill and method

A rolling mill system for Incremental rotary shaping of an elongated workpiece is provided that includes first and second workpiece holders. A support frame has a track with the first and second workpiece holders being movably associated with the track, the workpiece holders and an associated workpiece being movable in unison along the track. A radial chuck is mounted to the frame that includes a plurality of jaws that are movable radially inwardly and outwardly. Each jaw has a tool mounted thereto that is rotatable about an axis of rotation, with the axis of rotation of each tool being oriented at a skew angle relative to the longitudinal axis of a workpiece. A source of electric current and an electrically conductive flow path are provided for flowing electrical current through a workpiece. A controller is provided that is configured to control the operation of each of the first motor, second motor and third motor, and to control the flow of current flowing through the tools to the workpiece.

Zeng, Qiang↗
NASA NTRS1993

Active control of nonlinear-nonstationary response and radiation of a panel-stringer structure near a supersonic jet

This paper is on the control of nonlinear-nonstationary vibration of an aircraft-type frame-stringer structure and the acoustic radiation resulting from high levels of excitation by a nearby supersonic model jet exhaust. The objective of the control is to reduce the acoustic fatigue and the interior noise in a high-speed aircraft. Control of the structural response is achieved by actively forcing the structure with an actuator at the shock oscillation frequency whose amplitude is locked into a self-control cycle. This controller follows the amplitude modulation that results from the rotation and counter-rotation of the jet column. Results show that the peak level of the power in the structural response due to shock impingement is reduced by a factor of 63, corresponding to a power level reduction of 18 dB. As a result, new broadband components emerge with at least four harmonics contributing to the broadening of the response spectrum. At accelerating and decelerating supersonic speeds, the exhaust from the jet induces higher transient loading on the nearby flexible structure due to the occurrence of multiple shocks from the jet.

Maestrello, Lucio↗
NASA NTRS1989

Simulation and control problems in elastic robots

Computational issues associated with modeling and control of robots with revolute joints and elastic arms are considered. A manipulator with one arm and pinned at one end is considered to investigate various aspects of the modeling procedure and the model, and the effect of coupling between the rigid-body and the elastic motions. The rigid-body motion of a manipulator arm is described by means of a reference frame attached to the shadow beam, and the linear elastic operator denoting flexibility is defined with respect to this reference frame. The small elastic motion assumption coupled with the method of assumed modes is used to model the elasticity in the arm. It is shown that only terms up to quadratic in these model amplitudes need to be retained. An important aspect of the coupling between the rigid-body and the elastic motion is the centrifugal stiffening effect. This effect stiffens the elastic structure, as to be expected on physical grounds, gives rise to a time-varying inertia term for the rigid-body motion, and, in general, results in an effective inertia term smaller than the rigid-body inertia term. Simulation results are presented for an elastic beam pinned at one end and free at the other, and rotating in a horizontal plane, and control issues such as the order of the model, number of sensors, and modal extraction are examined within this context.

Tadikonda, S. S. K.↗
NASA NTRS1973

Comparative evaluation of ERTS imagery for resource inventory in land use planning

The author has identified the following significant results. Numerous previously unmapped faults in central Oregon have been distinguished on ERTS-1 imagery. Tectonic mapping of fault-controlled linears demonstrates the utility of ERTS-1 imagery as a mean of illustrating and studying the regional tectonics of the state. Soil colors observed on ERTS-1 frame 1075-18150-5 at the eastern end of the Columbia basin correlate very well with those from descriptions of soils from that area. Digital output from frame 1021-18151 has shown the enhanced ability to interpret such features as joint patterns, shadowed landslide blocks, bottomlands, and drainage patterns. Widespread use of wheat-fallow rotation in northern Umatilla County, Oregon, insures that nearly one-half of the cultivated soil is devoid of vegetation much of the time. On ERTS-1 imagery, fallow fields are only slightly darker than fields of wheat stubble at the western end of the transect. Similar climate-related contrasts in soil color are visible on ERTS-1 Imagery from several other portions of the Columbia Basin. Absence of steep topography in the area mentioned, however, minimizes the disturbing effect caused by shadows.

Simonson, G. H.↗
NASA NTRS1987

Slew maneuver dynamics of the Spacecraft Control Laboratory experiment

Mathematical expressions for slew maneuver dynamics are presented. The total kinetic energy expression of the system is given as T = T(0) + T(1) + T(2), where T(0), T(1), and T(2) refer to the kinetic energies of the shuttle, the flexible beam, and the tip mass (the reflector), respectively. The specific equations for each of these are defined and integrated into the total energy expression. Using the chain rule in the Lagrange equations and an expression allowing the transformation of the orbiter angular velocity from the inertial frame to the body-fixed frame, the rotational equations are obtained. Finally, the vibration equations for the beam are derived, again using the Lagrange equations.

Kakad, Y. P.↗
NASA NTRS1972

Four dimensional studies in earth space

A system of reference which is directly related to observations, is proposed for four-dimensional studies in earth space. Global control network and polar wandering are defined. The determination of variations in the earth's gravitational field with time also forms part of such a system. Techniques are outlined for the unique definition of the motion of the geocenter, and the changes in the location of the axis of rotation of an instantaneous earth model, in relation to values at some epoch of reference. The instantaneous system referred to is directly related to a fundamental equation in geodynamics. The reference system defined would provide an unambiguous frame for long period studies in earth space, provided the scale of the space were specified.

Mather, R. S.↗
NASA NTRS2010

Investigation of Rotor Performance and Loads of a UH-60A Individual Blade Control System

A full-scale wind tunnel test was recently conducted (March 2009) in the National Full-Scale Aerodynamics Complex (NFAC) 40- by 80-FootWind Tunnel to evaluate the potential of an individual blade control (IBC) system to improve rotor performance and reduce vibrations, loads, and noise for a UH-60A rotor system [1]. This test was the culmination of a long-termcollaborative effort between NASA, U.S. Army, Sikorsky Aircraft Corporation, and ZF Luftfahrttechnik GmbH (ZFL) to demonstrate the benefits of IBC for a UH-60Arotor. Figure 1 shows the UH-60Arotor and IBC system mounted on the NFAC Large Rotor Test Apparatus (LRTA). The IBC concept used in the current study utilizes actuators placed in the rotating frame, one per blade. In particular, the pitch link of the rotor blade was replacedwith an actuator, so that the blade root pitch can be changed independently. This concept, designed for a full-scale UH-60A rotor, was previously tested in the NFAC 80- by 120-FootWind Tunnel in September 2001 at speeds up to 85 knots [2]. For the current test, the same UH-60A rotor and IBC system were tested in the 40- by 80-FootWind Tunnel at speeds up to 170 knots. Figure 2 shows the servo-hydraulic IBC actuator installed between the swashplate and the blade pitch horn. Although previous wind tunnel experiments [3, 4] and analytical studies on IBC [5, 6] have shown the promise to improve the rotor s performance, in-depth correlation studies have not been performed. Thus, the current test provides a unique resource that can be used to assess the accuracy and reliability of prediction methods and refine theoretical models, with the ultimate goal of providing the technology for timely and cost-effective design and development of new rotors. In this paper, rotor performance and loads calculations are carried out using the analyses CAMRAD II and coupled OVERFLOW-2/CAMRAD II and the results are compared with these UH-60A/IBC wind tunnel test data.

Yeo, Hyeonsoo↗
NASA NTRS1992

An electronic pan/tilt/zoom camera system

A small camera system is described for remote viewing applications that employs fisheye optics and electronics processing for providing pan, tilt, zoom, and rotational movements. The fisheye lens is designed to give a complete hemispherical FOV with significant peripheral distortion that is corrected with high-speed electronic circuitry. Flexible control of the viewing requirements is provided by a programmable transformation processor so that pan/tilt/rotation/zoom functions can be accomplished without mechanical movements. Images are presented that were taken with a prototype system using a CCD camera, and 5 frames/sec can be acquired from a 180-deg FOV. The image-tranformation device can provide multiple images with different magnifications and pan/tilt/rotation sequences at frame rates compatible with conventional video devices. The system is of interest to the object tracking, surveillance, and viewing in constrained environments that would require the use of several cameras.

Zimmermann, Steve↗
NASA NTRS1995

Extension to the dynamic modeling of the large angle magnetic suspension test fixture

The Large Angle Magnetic Suspension Test Fixture (LAMSTF) is a laboratory scale proof-of-concept system. The configuration is unique in that the electromagnets are mounted in a circular planar array. A mathematical model of the system had previously been developed, but was shown to have inaccuracies. These inaccuracies showed up in the step responses. Eddy currents were found to be the major cause of the modeling errors. In the original system, eddy currents existed in the aluminum baseplate, iron cores, and the sensor support frame. An attempt to include the eddy current dynamics in the system model is presented. The dynamics of a dummy sensor ring were added to the system. Adding the eddy current dynamics to the simulation improves the way it compares to the actual experiment. Also presented is a new method of determining the yaw angle of the suspended element. From the coil currents the yaw angle can be determined and the controller can be updated to suspend at the new current. This method has been used to demonstrate a 360 degree yaw angle rotation.

Foster, Lucas E.↗
NASA NTRS2015

Modeling and Simulation of Vehicle Dynamics on the Surface of Phobos

In this paper we analyze the dynamics of a spacecraft in proximity of Phobos by developing the equations of motion of a test mass in the Phobos rotating frame using a model based on circularly-restricted three body problem, and by analyzing the dynamics of a ATHLETE hopper vehicle interacting with the soil under different soil-interaction conditions. The main conclusion of the numerical studies is that the system response is dominated by the stiffness and damping parameters of the leg springs, with the soil characteristics having a much smaller effect. The system simulations identify ranges of parameters for which the vehicle emerges stably (relying only on the passive viscoelastic damper at each leg) or unstably (needing active attitude control) from the hop. The implication is that further experimental and possibly computational modeling work, as well as site characterization (from precursor missions) will be necessary to obtain validated performance models.

soil-structure interaction↗
NASA NTRS1991

Coupled rotor-fuselage vibration reduction with multiple frequency blade pitch control

A nonlinear coupled rotor/flexible fuselage analysis has been developed and used to study the effects of higher harmonic blade pitch control on the vibratory hub loads and fuselage acceleration levels. Previous results, obtained with this model have shown that conventional higher harmonic control (HHC) inputs aimed at hub shear reduction cause an increase in the fuselage accelerations and vice-versa. It was also found that for simultaneous reduction of hub shears and fuselage accelerations, a pitch input representing a combination of two higher harmonic components of different frequencies was needed. Subsequently, it was found that this input could not be implemented through a conventional swashplate. This paper corrects a mistake originally made in the representation of the multiple frequency pitch input and shows that such a pitch input can be only implemented in the rotating reference frame. A rigorous mathematical solution is found, for the pitch input in the rotating reference frame, which produces simultaneous reduction of hub shears and fuselage acceleration. New insight on vibration reduction in coupled rotor/fuselage systems is obtained from the sensitivity of hub shears to the frequency and amplitude of the open loop HHC signal in the rotating reference frame. Finally the role of fuselage flexibility in this class of problems is determined.

Papavassiliou, I.↗
NASA NTRS2010

Magnetospheric Multiscale (MMS) Mission Attitude Ground System Design

This paper describes the attitude ground system (AGS) design to be used for support of the Magnetospheric MultiScale (MMS) mission. The AGS exists as one component of the mission operations control center. It has responsibility for validating the onboard attitude and accelerometer bias estimates, calibrating the attitude sensors and the spacecraft inertia tensor, and generating a definitive attitude history for use by the science teams. NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland is responsible for developing the MMS spacecraft, for the overall management of the MMS mission, and for mission operations. MMS is scheduled for launch in 2014 for a planned two-year mission. The MMS mission consists of four identical spacecraft flying in a tetrahedral formation in an eccentric Earth orbit. The relatively tight formation, ranging from 10 to 400 km, will provide coordinated observations giving insight into small-scale magnetic field reconnection processes. By varying the size of the tetrahedron and the orbital semi-major axis and eccentricity, and making use of the changing solar phase, this geometry allows for the study of both bow shock and magnetotail plasma physics, including acceleration, reconnection, and turbulence. The mission divides into two phases for science; these phases will have orbit dimensions of 1.2 x 12 Earth radii in the first phase and 1.2x25 Earth radii in the second in order to study the dayside magnetopause and the nightside magnetotail, respectively. The orbital periods are roughly one day and three days for the two mission phases. Each of the four MMS spacecraft will be spin stabilized at 3 revolutions per minute (rpm), with the spin axis oriented near the ecliptic north pole but tipped approximately 2.5 deg towards the Sun line. The main body of each spacecraft will be an eight-sided platform with diameter of 3.4 m and height of 1.2 m. Several booms are attached to this central core: two axial booms of 14.9 m length, two radial magnetometer booms of 5 m length, and four radial wire booms of 60 m length. Attitude and orbit control will use a set of axial and radial thrusters. A four-head star tracker and a slit-type digital Sun sensor (DSS) provide input for attitude determination. In addition, an accelerometer will be used for closed-loop orbit maneuver control. The primary AGS product will be a daily definitive attitude history. Due to power limitations, the star tracker and accelerometer data will not be available at all times. However, tracker data from at least 10 percent of each orbit and continuous DSS data will be provided. An extended Kalman filter (EKF) will be used to estimate the three-axis attitude (i.e., spin axis orientation and spin phase) and rotation rate for all times when the tracker data is valid. For other times, the attitude is generated by assuming a constant angular momentum vector in the inertial frame. The DSS sun pulse will provide a timing signal to maintain an accurate spin phase. There will be times when the Sun is occulted and DSS data is not available. If this occurs at the start or end of a definitive attitude product, then the spin phase will be extrapolated using the mean rate determined by the EKF.

Sedlak, Joseph E.↗
NASA NTRS2011

Magnetospheric Multiscale (MMS) Mission Attitude Ground System Design

This paper describes the attitude ground system (AGS) design to be used for support of the Magnetospheric MultiScale (MMS) mission. The AGS exists as one component of the mission operations control center. It has responsibility for validating the onboard attitude and accelerometer bias estimates, calibrating the attitude sensors and the spacecraft inertia tensor, and generating a definitive attitude history for use by the science teams. NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland is responsible for developing the MMS spacecraft, for the overall management of the MMS mission, and for mission operations. MMS is scheduled for launch in 2014 for a planned two-year mission. The MMS mission consists of four identical spacecraft flying in a tetrahedral formation in an eccentric Earth orbit. The relatively tight formation, ranging from 10 to 400 km, will provide coordinated observations giving insight into small-scale magnetic field reconnection processes. By varying the size of the tetrahedron and the orbital semi-major axis and eccentricity, and making use of the changing solar phase, this geometry allows for the study of both bow shock and magnetotail plasma physics, including acceleration, reconnection, and turbulence. The mission divides into two phases for science; these phases will have orbit dimensions of l.2xl2 Earth radii in the first phase and l.2x25 Earth radii in the second in order to study the dayside magnetopause and the nightside magnetotail, respectively. The orbital periods are roughly one day and three days for the two mission phases. Each of the four MMS spacecraft will be spin stabilized at 3 revolutions per minute (rpm), with the spin axis oriented near the ecliptic north pole but tipped approximately 2.5 deg towards the Sun line. The main body of each spacecraft will be an eight-sided platform with diameter of 3.4 m and height of 1.2 m. Several booms are attached to this central core: two axial booms of 14.9 m length, two radial magnetometer booms of 5 m length, and four radial -wire booms of 60 m length. Attitude and orbit control will use a set of axial and radial thrusters. A four-head star tracker and a slit-type digital Sun sensor (DSS) provide input for attitude determination. In addition, an accelerometer will be· used for closed-loop orbit maneuver control. The primary AGS product will be a daily definitive attitude history. Due to power limitations; the star tracker and accelerometer data will not be available at all times. However, tracker data from at least 10 percent of each orbit and continuous DSS data will be provided. An extended Kalman filter (EKF) will be used to estimate the three-axis attitude (i.e., spin axis orientation and spin phase) and rotation rate for all times when the tracker data is valid. For other times, the attitude is generated by assuming a constant angular momentum vector in the inertial frame. The DSS sun pulse will provide a timing signal to maintain an accurate spin phase. There will be times when the Sun is occulted and DSS data is not available. If this occurs at the start or end of a definitive attitude product, then the spin phase will be extrapolated using the mean rate determined by the EKF.

Sedlak, Joseph E.↗
DOE OSTI2022

Disruptive neoclassical tearing mode seeding in DIII-D with implications for ITER

New studies identify the critical parameters and physics governing disruptive neoclassical tearing mode (NTM) onset. An m/n = 2/1 mode in DIII-D that begins to grow robustly after a seeding event (edge localized mode ELM or sawtooth precursor and crash) causes the mode rotation to drop close to the plasma's Er = 0 rest frame; this condition opens the stabilizing ion-polarization current 'gate' and destabilizes an otherwise marginally stable NTM. Our new experimental and theoretical insights and novel toroidal theory-based modeling are benchmarked and scalable to ITER and other future experiments. Here, the nominal ITER rotation at q = 2 is found to be stabilizing ('gate closed') except for MHD-induced transients that could 'open the gate'. Extrapolating from the DIII-D ITER baseline scenario (IBS) discharges, MHD transients are much more likely to destabilize problematic robustly growing 2/1 NTMs in ITER; this makes predictions of seeding and control of both ELMs and sawteeth imperative for more than just minimizing divertor pulsed-heat loading.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2015

Iodine Satellite

The Iodine Satellite (iSat) spacecraft will be the first CubeSat to demonstrate high change in velocity from a primary propulsion system by using Hall thruster technology and iodine as a propellant. The mission will demonstrate CubeSat maneuverability, including plane change, altitude change and change in its closest approach to Earth to ensure atmospheric reentry in less than 90 days. The mission is planned for launch in fall 2017. Hall thruster technology is a type of electric propulsion. Electric propulsion uses electricity, typically from solar panels, to accelerate the propellant. Electric propulsion can accelerate propellant to 10 times higher velocities than traditional chemical propulsion systems, which significantly increases fuel efficiency. To enable the success of the propulsion subsystem, iSat will also demonstrate power management and thermal control capabilities well beyond the current state-of-the-art for spacecraft of its size. This technology is a viable primary propulsion system that can be used on small satellites ranging from about 22 pounds (10 kilograms) to more than 1,000 pounds (450 kilograms). iSat's fuel efficiency is ten times greater and its propulsion per volume is 100 times greater than current cold-gas systems and three times better than the same system operating on xenon. iSat's iodine propulsion system consists of a 200 watt (W) Hall thruster, a cathode, a tank to store solid iodine, a power processing unit (PPU) and the feed system to supply the iodine. This propulsion system is based on a 200 W Hall thruster developed by Busek Co. Inc., which was previously flown using xenon as the propellant. Several improvements have been made to the original system to include a compact PPU, targeting greater than 80 percent reduction in mass and volume of conventional PPU designs. The cathode technology is planned to enable heaterless cathode conditioning, significantly increasing total system efficiency. The feed system has been designed to include iodine compatible control valves with internal heaters and temperature sensors to coincide with the iodine-compatible thruster. A key advantage to using iodine as a propellant is that it may be stored in the tank as an unpressurized solid on the ground and before flight operations. During operations, the tank is heated to vaporize the propellant. Iodine vapor is then routed through custom flow control valves to control mass flow to the thruster and cathode assembly. The thruster then ionizes the vapor and accelerates it via magnetic and electrostatic fields, resulting in high specific impulse, characteristic of a highly efficient propulsion system. The iSat spacecraft is a 12-unit (12U) CubeSat with dimensions of about 8 inches x 8 inches x 12 inches (20 centimeters x 20 centimeters x 30 centimeters). The spacecraft frame will be constructed from aluminum with a finish to prevent iodine-driven corrosion. The iSat spacecraft includes full three-axis control and will leverage heat generated by spacecraft components and radiators for a passive thermal control system. After the CubeSat has successfully detached from its launch vehicle, it will deploy its solar panels, correct for tip-off and maintain attitude control before ground contact. An initial check-out period of two weeks is planned for testing all subsystems. The spacecraft will charge the power system while in sunlight, using momentum wheels and magnetic torque rods to rotate the vehicle to the required attitude.

iSat↗