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A possibility of an effective damping of rotor nutations by modulating the field of the moment transducers in synchronism with the nutation frequency is considered. The algorithms for forming the control moments are proposed and their application is discussed.
The kinetics of hypocotyl nutations in Helianthus annuus L. were measured on plants which were rotated on clinostats with axes of rotation inclined at various angles, alpha, away from the vertical. The g-force component acting in the direction of the plant axis was taken as g cos alpha. The average period and average amplitude of nutation were constant for all such axially directed g-forces between 1.0 and 0.2 g (vertical to about 80 inclination). On the horizontal clinostat (90 inclination) nutation was neither initiated nor sustained. The g-force just sufficient fully to activate nutational oscillations should be sought for g-force parameter values ranging from 0 to 0.2.
Passive device for damping nutational motion of spin stabilized Explorer XVII satellite
Rotational, precessional and nutational motion of body entering Mars atmosphere in vertical and oblique directions
Effects of precession and nutation in equator and equinox of earth
Precession and nutation of deformable bodies
Derivation of explicit equations governing deformations of self-gravitating viscous bodies in external force field for application to physical librations of moon
A centrifuge was used to provide sustained acceleration in order to study the hypocotyl nutation of 6-day-old Helianthus annuus L. over a range of g-forces, up to 20 times normal g. At the upper end of this g-range, nutation was impeded and at times was erratic evidently because the weight of the cotyledons exceeded the supportive abilities of the hypocotyls. Over the range 1 to 9 g, the period of nutation was independent of the resultant force vector. Over the same g-range, the amplitude of nutation was nearly independent of the chronic g-force. If nutation in sunflower seedlings is an oscillation caused by a succession of geotropic responses which continue to overshoot the equilibrium position (plumb line), its amplitude might be expected to be more sensitive to changes in magnitude of the sustained g-force. In order to preserve the geotropic model, in which nutation is considered to be a sustained oscillation driven by geotropic reactions, it is necessary to assume that geotropic response must increase with increasing g most rapidly in the region of the g-parameter below the terrestrial value of 1 g.
The design, computations, and testing of the nutation damper for the AMPTE-IRM satellite are described. The nutation motions of the satellite excite fluid oscillations in the closed tube system; kinetic energy is destroyed (converted to heat) through tube/fluid friction, constriction of the stream by cross sectional change, and formation of turbulence by stream enlargement. This energy is extracted from the satellite such that nutation is reduced. Tests were carried out in a pendulum testing device and the time constants were calculated. Findings showed that the damper remained within the originally specified values and provided for good dynamic behavior of the satellite.
An important goal of a tidal theory is the improvement of nutational amplitude and of the parameters of the earth's elastic response. A theory of tidal oscillations inside a rotating elliptical earth was developed, with special emphasis on tides in the liquid core. The Molodensky and Kramer theory of the resonance effect, as caused by the proximity of the frequency of the free diurnal wobble of the liquid core to the frequency of K sub 1 astronomical tide, was amended to include the effect of the possible deviation of the liquid core from the state of neutral stability. Coupling effects between the toroidal and spheroidal oscillations, as caused by the Coriolis force, were taken into consideration.
A face seal model consisting of a rigidly mounted rotor and a flexibly mounted stator was tested under conditions of eccentric loading. Self-excited oscillations in the form of combined precession and nutation of the stator were observed. The nature of the motion and its frequency are dependent on rotational speed, seal clearance, and external tilting moment. It is possible that some unexplained seal failures and waviness of seal faces are the result of such self excited wobble.
The communications antenna on a spin stabilized spacecraft is seldom located on the spin axis, hence, the antenna is in motion relative to the center of mass of the spacecraft. The Doppler shift observed at the ground or space relay communications receivers will include oscillations whose frequency and amplitude are functions of the motion of the antenna and the attitude of the spacecraft relative to the line of sight (LOS). This functional dependence creates the possibility of estimating attitude parameters from Doppler measurements. This paper presents mathematical models of Doppler oscillations from spinning spacecraft, including the effects of nutation. Algorithms for estimating spin rate, attitude and nutation angle are described. Results of analysis of Doppler tracking of GOES-8 and WIND are also discussed.
The mathematical theory of the nutation of Mars is derived by classical rigid-body dynamics. The effect of nutation is to produce a 26-m maximum horizontal amplitude oscillation (at the surface of Mars) with a period of half a Martian year. This effect should be detectable in the Viking-Lander data.
The controller design for the Solar Dynamics Observatory (SDO) is presented. SDO is a momentum biased spacecraft with three flexible appendages. Its primary scientific instrument, the solar oscillations imager (SOI), is rigidly attached to the spacecraft bus and has arc-second pointing requirements. Meeting these requirements necessitates the use of an active nutation controller (ANC) which is here mechanized with a small reaction wheel oriented along a bus transverse axis. The ANC does its job by orchestrating the transfer of angular momentum out of the bus transverse axes and into the momentum wheel. A simulation study verifies that the controller provides quick, stable, and accurate response.
The Liquid Motion Experiment (LME), which flew on STS 84 in May 1997, was an investigation of liquid motions in spinning, nutating tanks. LME was designed to quantify the effects of such liquid motions on the stability of spinning spacecraft, which are known to be adversely affected by the energy dissipated by the liquid motions. The LME hardware was essentially a spin table which could be forced to nutate at specified frequencies at a constant cone angle, independently of the spin rate. Cylindrical and spherical test tanks, partially filled with liquids of different viscosities, were located at the periphery of the spin table to simulate a spacecraft with off-axis propellant tanks; one set of tanks contained generic propellant management devices (PMDs). The primary quantitative data from the flight tests were the liquid-induced torques exerted on the tanks about radial and tangential axes through the center of the tank. Visual recordings of the liquid oscillations also provided qualitative information. The flight program incorporated two types of tests: sine sweep tests, in which the spin rate was held constant and the nutation frequency varied over a wide range; and sine dwell test, in which both the spin rate and the nutation frequency were held constant. The sine sweep tests were meant to investigate all the prominent liquid resonant oscillations and the damping of the resonances, and the sine dwell tests were meant to quantify the viscous energy dissipation rate of the liquid oscillations for steady state conditions. The LME flight data were compared to analytical results obtained from two companion IR&D programs at Southwest Research Institute. The comparisons indicated that the models predicted the observed liquid resonances, damping, and energy dissipation rates for many test conditions but not for all. It was concluded that improved models and CFD simulations are needed to resolve the differences. This work is ongoing under a current IR&D program.