The elements of a spacecraft with axial mass symmetry and a reaction-wheel ontrol system are shown in the figure. When the motor exerts a torque on the eaction wheel, an equal and opposite torque is exerted on the spacecraft, hereby changing its angular momentum in the z-direction. We want to change he orientation of the spacecraft about the z-axis by an amount of 0 by applying CONSTANT torque M to the motor of the reaction wheel in either direction positive and then negative z directions) as shown in the below graph. The ystem starts initially from rest and the maneuver is completed after time tm . After the maneuver is completed the system returns to rest condition. Mass of he spacecraft (including the wheel) is ms , and radius of gyration about z is kszi nd the mass of the reaction wheel mw , and radius of gyration about z is kwz. he spin axis of the wheel is coincident with the z-axis of symmetry of the pacecraft. Determine the the time to reverse the torque, ti, and the constant orque M required for this maneuver.
The elements of a spacecraft with axial mass symmetry and a reaction-wheel ontrol system are shown in the figure. When the motor exerts a torque on the eaction wheel, an equal and opposite torque is exerted on the spacecraft, hereby changing its angular momentum in the z-direction. We want to change he orientation of the spacecraft about the z-axis by an amount of 0 by applying CONSTANT torque M to the motor of the reaction wheel in either direction positive and then negative z directions) as shown in the below graph. The ystem starts initially from rest and the maneuver is completed after time tm . After the maneuver is completed the system returns to rest condition. Mass of he spacecraft (including the wheel) is ms , and radius of gyration about z is kszi nd the mass of the reaction wheel mw , and radius of gyration about z is kwz. he spin axis of the wheel is coincident with the z-axis of symmetry of the pacecraft. Determine the the time to reverse the torque, ti, and the constant orque M required for this maneuver.
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All the units in centimeter must be transformed into meter, and degree into radian.!!!BE CAREFUL ABOUT THE UNITS!!!
Transcribed Image Text:The elements of a spacecraft with axial mass symmetry and a reaction-wheel
control system are shown in the figure. When the motor exerts a torque on the
reaction wheel, an equal and opposite torque is exerted on the spacecraft,
thereby changing its angular momentum in the z-direction. We want to change
the orientation of the spacecraft about the z-axis by an amount of 0 by applying
Reaction
Wheel
a CONSTANT torque M to the motor of the reaction wheel in either direction
(positive and then negative z directions) as shown in the below graph. The
Moter
system starts initially from rest and the maneuver is completed after time tm .
After the maneuver is completed the system returns to rest condition. Mass of
M (torque)
the spacecraft (including the wheel) is ms , and radius of gyration about z is kszi
Mo
and the mass of the reaction wheel mw , and radius of gyration about z is kwz.
The spin axis of the wheel is coincident with the z-axis of symmetry of the
t (time)
spacecraft. Determine the the time to reverse the torque, tı, and the constant
torque M required for this maneuver.
-M.
Os = - 48 degree, tm = 28 s , ms = 190 kg , ksz = 25 cm, mw = 1.2 kg , kwz = 9 cm
Negative Os value means that we want to rotate the satellite in clockwise direction when looking from up to
down (z towards the origin).
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