Nutation Damper Research Articles

A Semi-Active Nutation Damper for Spinning Prolate or Oblate Satellites

A nutation damper is proposed which will damp nutation of spinning prolate satellites. It consists of a compliant flywheel (a canister of fluid is suggested) spun by an electric motor at high speed in the opposite direction to the satellite spin, about an axis parallel to the spin axis. It is shown first of all that it operates in a regime which fits in with previous theory. Its performance is predicted, and it is shown that it will also damp the nutation of an oblate body, or cause a spherical body to spin about a preferred axis. It is shown that the mechanical efficiency of such a device is low, but that this does not rule out its usefulness for most purposes.

Stability, instability, and terminal attitude motion of spinning, dissipative spacecraft

This paper deals with the following questions: What is the physical significance of the words ''stability and as used in connection with attitude motions of a spacecraft carrying a passive nutation damper? What is the nature of the terminal motion of the spacecraft? To answer these questions, stability criteria are formulated in analytical terms, numerical integrations of differential equations governing system behavior are performed, and both qualitative and quantitative descriptions of terminal motions are formulated. Numerical results are displayed in the form of time-plots of the angle between a spacecraft-fixed line and a space-fixed line, and these reveal that instability may be attributable to a variety of causes and may manifest itself in a variety of ways. Two types of terminal motion associated with instabilities arising from energy dissipation are discussed in detail.

Method for evaluating gravity effects in the testing of nutation dampers

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Active control of the dynamics of a dual-spin spacecraft

Active damping of both vehicle nutation and payload flexibility for a dual-spin spacecraft is achieved using the interaction of the vehicle dynamics with the on-board despun payload control system. A closed-form solution to the interaction problem is presented, deriving an analytical expression which is used to establish both the fundamental stability and the strength of the coupling. Analysis of the characteristics of the interaction leads to mass property and control system design criteria which can be used to effectively optimize the interaction and provide substantial active control. Design examples are presented which illustrate the design techniques involved in the optimization. Simulation results are presented which verify the analytical conclusions.

Design and ground test of a pendulum-type active nutation damper

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Circularly Constrained Particle Motion in Spinning and Coning Bodies

The motion of a particle constrained to move on a circular path within a body that is spinning and coning is examined. The equation governing this motion is expressed as a nonlinear, nonautonomous ordinary differential equation, and the behavior of solutions of this equation is investigated using phase plane techniques. Several classes of phase plane portraits are identified, and boundaries that separate system parameters giving rise to portraits of each class are established. Practical applications for the information thus generated include the analysis and design of certain passive balancing devices used to attenuate wobble in spinning spacecraft and the study of simplified models of nutation dampers and thermal control devices consisting of circular tubes partially filled with fluid.

Comments on "Analytical Design of Optimal Nutation Dampers"

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Partially Filled Viscous Ring Nutation Damper

The problem of a spinning satellite with a partially filled viscous ring nutation damper is investigated. It is shown that there are two distinct modes of motion, previously named the nutation synchronous mode and the spin synchronous mode. An approximate solution for the nutation angle time history is obtained and time constants for the two modes are given as a function of suitable dimensionless parameters. Comparison is then made with the exact solution obtained by numerical integration of the exact equations of motion. From a consideration of the fluid dynamics several methods are developed for determining the damping constant.

Active Nutation Damping Utilizing Spacecraft Mass Properties

Active nutation damping generally requires a unique element to provide the necessary damping torques, plus a nutation-sensing system to properly monitor and control the active element by closed-loop action. This paper describes and analyzes, by computer- assisted mathematical techniques, a nutation damper for a dual-spin spacecraft which does not require an active ?element?. Damping is achieved through the inherent cross-axis torques generated by the spacecraft products of inertia and the existing motor controlling the relative spin rates of the two dynamic components comprising the spacecraft.

Solar Pressure Control of a Dual-Spin Satellite

Nutation damping and attitude control of a spinning satellite using solar radiation pressure is studied for the general case of attutide motion in an arbitrary orbit. The nonlinear, nonautonomous, coupled equations of motion involving large numbers of parameters are only amenable to a numerical approach. The response data, presented as functions of the system parameters, show the controller's effectivenss in damping the most severe disturbances in a fraction of an orbit. The controller provides versatility to the satellite, enabling it to change its preferred orientation in orbit and, hence, undertake diverse missions. An illustrative example using mass properties representative of INTELSATIV and the Canadian communications satellite (Anik-1) demonstrates the feasibility of the concept. The semipassive character promises an increased lifetime with an effective reduction in cost.

Attitude Dynamics of a "Nearly Spherical" Dual-Spin Satellite and Orbital Results for OSO-7

T take advantage of the increased capability of the Delta launch vehicle, major design changes were made in the latest dual-spin stabilized Orbiting Solar Observatory (OSO7). Changes in observatory size and shape, and in the launch sequence, accentuated the effects (on spin axis coning) of certain mass properties and of motions of the nutation damper and solar-pointed instruments. These effects are described using digital computer simulations and force-balance and energy-sink calculations. The familiar energy-sink stability condition for dual-spin satellites is generalized to account for platform asymmetries. The excellent orbital performance of OSO-7 lends over-all support to the analyses.

Nutation dampers vs precession dampers for asymmetric spinning spacecraft.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

The Use of a Spinning Dissipator for Attitude Stabilization of Earth-Orbiting Satellites

This paper considers a novel attitude stabilizing system which acts both as a passive nutation damper and a momentum source for an Earth-orbiting satellite. The system may be designed to use four identical wheels mounted coaxially with and at the ends of the arms of a cruciform structure. The structure may then be spun about the axis perpendicular to the arms to provide angular momentum along the spacecraft spin axis. The wheels experience torques produced by inertial forces. The necessary damping and restoring (spring) torques are provided by means of a torsional arrangement built around the center of each wheel. The performance characteristics of the proposed stabilizing unit are evaluated by considering spacecraft parameters used in one phase of development of the Communications Technology Satellite (CTS). The results obtained for a specific design of the stabilizer indicate that global stability of the desired attitude motion of the spacecraft can be guaranteed with associated damping time constant as low as one second.

On the existence of a trap state for OSO-type satellites

The possibility of the existence of "trap states" in orbiting-solar-observatory-type satellites which use a single-degree-of-freedom mass-spring-dashpot nutation damper is investigated. It is shown that the spacecraft exhibits a trap state which corresponds to a transverse angular rate of ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> , where ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> denotes the natural frequency of the specific damping system used. In particular, it is indicated that for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{10} &lt; \omega_{n}</tex> , where ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</inf> is the initial transverse angular rate of the spacecraft, a trap state occurs when the initial displacement z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> of the damper mass with respect to the spacecraft principal axis exceeds a certain critical value; while for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{10} &gt; \omega_{n}</tex> , the trap state occurs for any nonzero value of z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> .

Creep in the earth and planets

Evidence of imperfectly elastic behaviour in the earth and planets is provided by the following phenomena: 1. (1) damping of the earth's free nutation; 2. (2) damping of elastic waves passing through the earth; 3. (3)secular acceleration of the moon; 4. (4) figure of the moon; 5. (5) figure of the earth; 6. (6) rotations of satellites of the planets; 7. (7) free oscillations of the directions of the moon's axes; 8. (8) eigenfrequencies of the earth; and 9. (9) damping of the S wave as a function of frequency. Darwin attempted to explain the secular acceleration of the moon by viscosity in the body of the earth. This was shown to be unsatisfactory in 1915. A logarithmic law of creep, containing one relevant constant, agrees with some laboratory tests and approximately with a large quantity of seismological data. But it was found that if the constant is chosen to fit the damping of the free nutation (Eulerian nutation or Chandler wobble) the beginning of a transverse seismic wave at distance 80° would be spread over about 70 sec and be unreadable. I propose a law of creep by which for a constant shearing stress P the response is a shearing strain ϵ given by: ϵ = P μ [1 + q α {(1 + at) α − 1 ]} where t is time and μ, q, a, α are constants. This is a particular case of imperfection of elasticity. In it, for disturbances lasting a second or more, there are essentially only two creep parameters to be fixed, α and qa α . These may be determined by the two data: 1. (1) that the relaxation time of the free nutation is 30 ± 20 yyears; 2. (2) that S at 80° reaches half its ultimate value in 2 sec. We obtain α as probably between 0.14 and 0.21, with 0.19 as the most probable value. We then proceed to show that this law of creep, with α = 0.19, can account for approximately the right amount of damping (or internal friction) in all the other phenomena listed above. Laws with α = 1 (elastico-viscous law) and α = 0 (logarithmic law) fail to do so. A consequence of this law of creep is that where it holds convection cannot take place.

Creep in the Earth and Planets (Invited Lecture)

An outstanding problem is to reconcile the Moon's rotation with the persistence of its non-hydrostatic dynamical ellipticities. The first requires imperfection of elasticity under strains of order 10−7; the second apparently little under larger ones.Lomnitz gave experimental evidence that creep is linear at elastic shears from 10−5to 10−4, indicating that a linear rule could be right at still smaller values. Positive evidence for the Earth comes from the damping of the 14-monthly nutation, which has a relaxation time of the order of 30 yr. Most work on imperfect elasticity has assumed that under constant shear stress the strain increases with time either liket(elasticoviscosity) or like logt.If the result from the 14-monthly nutation, with elasticoviscosity, is applied to the Moon, the dynamical ellipticities would have subsided considerably in the last 200 yr. With the logarithmic rule anSpulse at 80° would have its beginning spread out over about 70 s and be unreadable. These contradictions are avoided if the increase under constant stress is about liket0.2. The resulting law involves two constants. Without change of these, applications are made to other phenomena. The rotations of the Moon and of other satellites whose rotations are known are explained; so is the persistence of the Moon's dynamical ellipticities; also the failure to detect three free oscillations that might theoretically exist. Elasticoviscosity would imply rapid disappearance of the non-hydrostatic second and third harmonics in the Earth's gravitational field; this is avoided with the new law. Study of damping of free vibrations of the Earth (including surface waves) has usually assumed the logarithmic law, but it appears that the new law fits the data at least as well, and that it may also explain those that have been interpreted in favour of layers of low velocity. It appears that the damping at depths up to 400 km or so is much more severe than the average for the Earth's shell, and more evidence for shorter periods is much needed.Any law with an index less than 1 would forbid thermal instability (convection) and continental drift.

Attitude Motion of a Nutationally Damped Dual-Spin Spacecraft in the Presence of Near-Earth Environment

T effect of both gravity-gradient torques and the nearEarth environment on the attitude motion of a dual-spin spacecraft with nutation damper is predicted by digital simulation. The program employs a geometrical modeling technique to determine the total unshadowed spacecraft surface area required for the computation of aerodynamic torques. In addition, the deliberate steering of the satellite spin axis with magnetically induced torques is described.

Nutation damping and vibration isolation in a flexibly coupled dual-spin spacecraft

As the accuracies required to meet mission objectives become increasingly greater, the suitability of the dual-spin concept rests more and more on its ability to provide a platform free of extraneous motion. This paper is concerned with the possibility of achieving this goal by introducing a flexible, dissipative coupling between the platform and rotor of such a spacecraft. Both analytical and numerical results are presented, and it is shown, for realistic spacecraft designs, throughout that settling times for damping nutation of the order of a few seconds may be obtained, while at the same time, platform vibrations induced by static and dynamic unbalances in the rotor are attenuated by a factor of three or more.

Variable Parameter Nutation Damper for SAS-A

This paper presents design objectives, functional description and in-flight performance of a variable parameter nutation damper for a dual-spin satellite. The damper consists of a torsion wire mounted pendulum which includes the capability of command changing the pendulum resonant frequency and damping constant in order to obtain optimum spin axis stabilization for both a dual-spin and single-spin spacecraft dynamical condition. State-of-theart features of this damper include: 1) taut-band suspension, for a pendulous mass, which has no mechanical friction of hysteresis, 2) magnetic circuit for changing the torque constant of the taut-band thereby changing the damper natural frequency, 3) chargeable magnet system for varying the damping coefficient, and 4) 7-bit optical readout for telemetering the damper motion. The damper weights 2.7 Ib and draws 20 mw power when functioning for dual-spin conditions. The minimum nutation damping time constant in this mode is 12 min with a predicted spin axis pointing accuracy of 1 min of arc. Stabilization to better than 2 min of arc has been achieved in orbit.

Parameter Optimization of a Nutation Damper Via the Second Method of Liapunov

The principle of parameter optimization of a linear time-invariant system via the second method of Liapunov is applied to optimize the parameters of a nutation damper suggested recently. Numerical results are derived, and it is indicated that the present values of optimum parameters agree closely with those obtained earlier by an approximate method.