Both in orbit and during orbit insertion, spacecraft and upper stage vehicles are frequently provided with spin to ensure attitude stability. At other times it may be necessary to terminate the spin permanently or at least temporarily, for example, to reorient the vehicle prior to a propellant burn. Despinn-ing can be accomplished by firing small retro-rockets mounted on the vehicle such as to produce a torque counter to the direction of spin. Alternatively, despin can be obtained by initiating the so-called yo-yo mechanism discussed in the following.

This type of despin is frequently used in the case of cylindrically shaped vehicles. It has the advantage of great simplicity and reliability. As indicated in Fig. 1.6, one or several weights are attached to cables that are initially wrapped around the vehicle, typically in the plane through the vehicle's center of mass and normal to the spin axis (which is also one of the principal axes of inertia). Initially, the weights are attached to the body of the vehicle. Despin is initiated by releasing the weights pyrotechnically. As the cables now unwrap, the weights swing out on a path that is an involute of a circle when viewed in a reference frame corotating with the vehicle. The sense of the initial wraparound is such that the pull of the cables reduces the vehicle's angular momentum. When the cables are fully extended, a split hinge releases them and the weights.

The following analysis applies to a system with two symmetrically arranged weights, each of mass m. (Xi, X2) designates an inertial reference frame. The frame (xi, X2) with the corresponding unit base vectors Ui and u2 is moving with the instantaneous location of the tangent point O of the cable. The angular velocity of the vehicle is designated by Q(t), and f(t) is the angle between the weight attachment/release point and the cable's

Path of m relative to spacecraft

Attach ment/release of m

Attachment/releaseof cable Spacecraft

Figure 1.6 Schematic of despin yo-yo mechanism.

Path of m relative to spacecraft

Attach ment/release of m

Attachment/releaseof cable Spacecraft

Figure 1.6 Schematic of despin yo-yo mechanism.

tangent point. Hence the angular velocity of the (jci, x2) reference frame is

The free length of the cable is Rof, where R0 is the radius of the spacecraft. The position vector for the point mass m in the (X\, x2) frame is r = Roirui, andR = R0{f Ui +u2) in the {Xu X2) system. From (1.2) then follows

The total angular momentum L of the vehicle and the two masses is in the direction of the X3 axis and is given by

where is the vehicle's moment of inertia about the spin axis. Hence

With the initial condition f - 0 at t = 0, it follows from the constancy of L that fc(£20 - £2) = ir2co (1.8)

1.3 Example: The Yo-Yo Despin Mechanism

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