lecture23 - Torques and their sources Torques may be •...

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Unformatted text preview: Torques and their sources Torques may be • External: interaction with the outside world. May be natural or may be generated inside spacecraft, e.g., thrusters. • Internal: acting totally inside the space- craft; they must all cancel out. Neverthe- less, they are useful as angular momentum can be shifted from a part of concern (the spacecraft as a whole) to something else (flywheel). L. Healy – ENAE404 – Spring 2007 – Lecture 23 (Apr. 19) 1 Attitude control of spinning spacecraft Ref.: Curtis Sec. 10.6, Wiesel Sec. 5.5. The coning (nutation) behavior described be- fore can be exploited to reorient an axisymmet- ric spacecraft spinning on its axis by applying external torque. • Apply impulsive torque (with off-center thrusters) perpendicular to axial spin. • Let axis precess through an angle of π . • Apply another torque identical in magni- tude and orientation relative to the space- craft to stop precession. Like orbital ma- neuver. • To change H through an angle θ requires Δ H = 2 H tan θ , meaning change of θ = 90 ◦ is infinitely expensive. • Make series of small coning maneuvers, less expensive, but takes longer. • Compromise: several intermediate. L. Healy – ENAE404 – Spring 2007 – Lecture 23 (Apr. 19) 2 Torque-controlled motion If we don’t use propulsion, the only external torque will have to come from natural sources. There are two kinds of natural torque that can be used to control the attitude of a spacecraft: • Magnetic stabilization: with a magnetic coil “torque rod” in the spacecraft, use the Earth’s magnetic field to alter the attitude. See Chobotov Chapter 8. • Gravity gradient: gradient of Earth’s grav- itational field and shape of spacecraft to stabilize the attitude in an orbit reference frame. L. Healy – ENAE404 – Spring 2007 – Lecture 23 (Apr. 19) 3 Gravity gradients Ref.: Curtis Section 10.10, Wiesel Section 5.8 Satellite is usually torque-free, except close to a planet where it can experience a gravity gra- dient torque . This is a torque induced by dif- fering gravitational pull on different parts of the satellite. A satellite with unequal moments of inertia will experience a torque that aligns the axis of least moment inertia in the direction of center of the attracting mass. L. Healy – ENAE404 – Spring 2007 – Lecture 23 (Apr. 19) 4 Coordinates and lengths • The attracting force is along the line from the center of mass of the body towards the center of the earth. • r is the vector from the center of earth to the c.m. of the spacecraft, as always. Curtis calls this r . • s is the vector of any point in the space- craft from its c.m., so s r . Curtis calls this ρ ....
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lecture23 - Torques and their sources Torques may be •...

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