Analysis of pendulum damper for satellite wobble damping

Alper, Joel

doi:10.2514/6.1964-93

Cited by 5 publications

(4 citation statements)

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“…2d, positions of pendulums 1-3). There are three essentially different equilibrium positions of the pendulums on the lower plane: k k 1 Combining these positions, we obtain nine essentially different steady motions.…”

Section: Restrictions Of the Problemmentioning

confidence: 99%

“…Attitude stabilization of the rotational axis of a carrying perfectly rigid body (PRB) is an important problem of mechanics. Such bodies can be artificial satellites or spacecraft with spin stabilization [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Spin stabilization is disadvantageous in that, for example, inaccurate initial rotation imparted to a symmetric satellite causes its rotational axis to long precess about a fixed axis (axis of precession).…”

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confidence: 99%

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Attitude stabilization of the rotational axis of a carrying body by pendulum dampers

2007

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The paper addresses attitude stabilization of the rotational axis of an asymmetric carrying body by pendulum dampers. Steady motions in which the kinetic energy of the system takes stationary values are identified. Whether these motions are stable is established Keywords: stabilization, rotational axis, asymmetric carrying body, pendulum dampers, kinetic energy Introduction. Attitude stabilization of the rotational axis of a carrying perfectly rigid body (PRB) is an important problem of mechanics. Such bodies can be artificial satellites or spacecraft with spin stabilization [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Spin stabilization is disadvantageous in that, for example, inaccurate initial rotation imparted to a symmetric satellite causes its rotational axis to long precess about a fixed axis (axis of precession). To suppress the nutation, various dampers are applied. It was shown in [1, 3, 6, 7, 12] that pendulums and viscous dampers effectively decrease rather large initial nutation angles of the PRB rotation axis. However, the reasons for the residual nutation of this axis have not yet been established. The fundamental possibility to completely damp nutation with pendulum dampers was pointed out in [13,14]. This possibility has not been examined so far. In this connection, the present paper looks into the attitude stabilization of the rotational axis of a PRB with pendulum dampers. Namely, steady motions of the system will be identified, it will be established whether these motions are stable, and the possibility of complete dampening of nutation with dampers will be examined.Closely related issues are considered in [15][16][17][18]. We will consider a damper consisting of two pairs of pendulums set onto an axis rigidly fixed to the PRB. The theory of passive automatic balancers [9] suggests that such a device can completely counterbalance a nonsymmetric PRB and, thereby, completely damp nutation.1. Model Description. Consider a PRB of mass Ì. The mass and inertia characteristics of the PRB and the whole system will be described using the principal axes of inertia OXYZ, with the origin O at the centroid of the PRB (Fig. 1a). The axial moments of inertia about the X-, Y-, and Z-axes are denoted by A, B, and C, respectively. In the general case, we have À Â Ñ ¹ ¹ .

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Section: Restrictions Of the Problemmentioning

confidence: 99%

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confidence: 99%

Attitude stabilization of the rotational axis of a carrying body by pendulum dampers

2007

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“…(7). The apparent spring constant of the damper is diminished by the centrifugal force due to spin about the z axis (the co 2 2 term) and also by the contribution of the cross spin centrifugal force (the co y 2 term). Although the latter term may be small compared to the first terms, it cannot be neglected, since this periodic force can cause parametric excitation of the damper mass motion.…”

Section: Substituting Into Euler's Equationsmentioning

confidence: 99%

Nutation damper instability on spin-stabilized spacecraft

Cloutier

1969

AIAA Journal

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The dynamic equations describing the motion of a single-degree-of-freedom nutation damper mounted on a dual-spin spacecraft are examined. The motion of the damper mass is found to be parametrically excited by the transverse angular rates, so that instabilities of this motion are possible. In this situation, instability could imply that the damper mass moves to an extreme position and remains there; hence, it would not perform its intended function of dissipating energy in order to damp out nutation. It is found that this unstable behavior is quite possible for a damper mounted on a single-spin spacecraft or on the spinning portion of a dual-spin spacecraft where the other member is essentially despun. On the other hand, unstable behavior of a damper mounted on the despun member of a dual-spin configuration is found to be extremely unlikely. D H M P a b c d,e f n k m v 5,e f 6 Nomenclature = moments of inertia, slug ft 2 (ft-lb-sec 2 )= angular momentum ratio = angular momentum, ft-lb-sec = moment, ft-lb = amplitude of angular velocities, rad/sec = acceleration, ft /sec 2 = length, ft = damping constant, Ib-sec/ft = parameters = natural frequency, rad/sec = spring constant, Ib/ft = mass, slugs (Ib-sec 2 /ft) = velocity, fps = parameters = damping ratio = wobble angle, rad = characteristic exponent

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“…Finally, let the spring (and hence A) be undefprmed when P lies on G 2 and choose 6, the distance between L and G*, m p , the mass of P, m G , the mass of G, and 7 7 , 7 2 , I 3 , the moments of inertia of G about G/, G 2 , G 3 , in such a way that where /* is defined as A I 2 =I 3 +pb 2 =J 2 p +m G ) (7) (8) If these requirements are fulfilled, it is guaranteed that when A is undeformed, the central inertia ellipsoid of S is a spheroid whose axis is parallel to g lt the moment of inertia of S about the line passing through S* and parallel to gj is equal to /;, and the moment of inertia of S about any line passing through S* and perpendicular to gj is equal to J 2 . Fur- thermore, the angular momentum of S relative to S* is then given, for all /, by H=H lg] +H 2 g 2 +H 3 g 3 provided H lt H 2 , H 3 be defined as (9) (10) (11) (12) where q is the distance from P to G 2 (see Fig. 4) and (f ) i = N u R .…”

Section: Tt)mentioning

confidence: 99%