SEARCH · Search NASA

Results for “nutation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

All sources NASA NTRS DOE OSTI

NASA NTRS1995

An a priori model for the reduction of nutation observations: KSV(1994.3) nutation series

We discuss the formulation of a new nutation series to be used in the reduction of modern space geodetic data. The motivation for developing such a series is to develop a nutation series that has smaller short period errors than the IAU 1980 nutation series and to provide a series that can be used with techniques such as the Global Positioning System (GPS) that have sensitivity to nutations but can directly separate the effects of nutations from errors in the dynamical force models that effect the satellite orbits. A modern nutation series should allow the errors in the force models for GPS to be better understood. The series is constructed by convolving the Kinoshita and Souchay rigid Earth nutation series with an Earth response function whose parameters are partly based on geophysical models of the Earth and partly estimated from a long series (1979-1993) of very long baseline interferometry (VLBI) estimates of nutation angles. Secular rates of change of the nutation angles to represent corrections to the precession constant and a secular change of the obliquity of the ecliptic are included in the theory. Time dependent amplitudes of the Free Core Nutation (FCN) that is most likely excited by variations in atmospheric pressure are included when the geophysical parameters are estimated. The complex components of the prograde annual nutation are estimated simultaneously with the geophysical parameters because of the large contribution to the nutation from the S(sub 1) atmospheric tide. The weighted root mean square (WRMS) scatter of the nutation angle estimates about this new model are 0.32 mas and the largest correction to the series when the amplitudes of the ten largest nutations are estimated is 0.18 +/- 0.03 mas for the in phase component of the prograde 18. 6 year nutation.

Herring, T. A.↗

NASA NTRS1972

The SAS-D nutation control system

A control law is developed for the SAS-D nutation control system. Nutation is removed in a sub-optimal manner with respect to fuel consumed, but attitude errors are minimized. The research performed consist of an investigation of nutation theory and nutation due to energy dissipation, nutation detection analysis, nutation control analysis, and error analysis. The resulting nutation control system uses an accelerometer or rate gyro to sense the nutation angle theta which varies sinusoidally at the nutation frequency omega. The sensed nutation angle is compared with a threshold theta sub tau. If the sensed nutation is greater, a thrust pulse of duration equal to the period of one spin cycle is initiated. Since the threshold theta sub tau is set equal to the amount of nutation that can be removed by one thrust pulse of duration equal to one spin cycle, the spacecraft nutation is reduced to near zero. Error analysis indicates that the nutation sensed, the threshold, the amount of nutation that can be removed during one thrust pulse, and the time duration of one thrust pulse are all sensitive to the spacecraft spin frequency imparted by the Delta rocket. Thus, the nutation control system was designed to be adaptive to the possible variations in imparted spin frequency.

Taylor, J. M.↗

NASA NTRS1995

Precession and nutation from joint analysis of radio interferometric and lunar laser ranging observations

24 years of Lunar Laser Ranging (LLR) observations and 16 years of Very Long Baseline Interferometry (VLBI) observations are combined in a global analysis to yield improved estimates of the Earth's precession and nutation. The correction to the International Astronomical Union (IAU) (1976) precession constant inferred from this joint VLBI/LLR analysis is -3.00 +/- 0.20 milliarcsec/yr (mas/yr). A significant obliquity rate correction of -0.20 +/- 0.08 mas/yr is also found. In all, 32 forced nutation coefficients are estimated. These coefficients confirm that the IAU (1980) nutation theory is in error by several mas. The estimated nutation coeficients are found to vary by as much as several tenths of mas, depending on the a priori nutation model used to analyze the VLBI and LLR data. Forced circular nutations derived from this analysis agree with the ZMOA-1990-2 nutation theory at the 0.2 mas level for the 18.6 yr terms, and at the 0.05 mas level for the other terms (periods less than or = 1 yr). A retrograde free core nutation with an amplitude of 0.20 mas is also detected. Its phase is found to be very sensitive to the precise value of the free core nutation period used in the solution. Separate analyses of four independent subsets of the LVBI data indicate no significant variations of the free core nutation since 1988. The pre-1988 estimates of the free core nutation are consistent with the post-1988 estimates but are not accurate enough to rule out possible variations of the free core nutation at these earlier epochs.

Charlot, P.↗

NASA NTRS1974

Testing a satellite automatic nutation control system

Testing of a particular nutation control system for the synchronous meteorological satellite (SMS) is described. The test method and principles are applicable to nutation angle control for other satellites with similar requirements. During its ascent to synchronous orbit, a spacecraft like the SMS spins about its minimum-moment-of-inertia axis. An uncontrolled spacecraft in this state is unstable because torques due to fuel motion increase the nutation angle. However, the SMS is equipped with an automatic nutation control (ANC) system which will keep the nutation angle close to zero. Because correct operation of this system is critical to mission success, it was tested on an air-bearing table. The ANC system was mounted on the three-axis air-bearing table which was scaled to the SMS and equipped with appropriate sensors and thrusters. The table was spun up in an altitude chamber and nutation induced so that table motion simulated spacecraft motion. The ANC system was used to reduce the nutation angle. This dynamic test of the ANC system met all its objectives and provided confidence that the ANC system will control the SMS nutation angle.

Hrasiar, J. A.↗

NASA NTRS1980

Active nutation controller

An apparatus is described for controlling nutation motion in a spinning body, comprised of an angular accelerometer with its input axis perpendicular to the spin axis of the body, a flywheel with an axis of rotation perpendicular to the axis of the accelerometer and to the spin axis of the body, and a motor for driving the flywheel to attenuate or build nutation. The motor is controlled by circuitry that monitors the output of the angular accelerometer and drives the motor clockwise or counterclockwise during predetermined nutation angles synchronized to the zero crossover points of the accelerometer signal centered about the nutation peaks. The motor drive is phased to damp nutation motion to zero for stabilization. To increase the noise immunity of the system, when the output of the accelerometer falls below a threshold level, the circuitry operates in an open loop, beat mode where data representing the last accelerometer signal that exceeded that threshold level is stored, and the motor drive is controlled by the stored data. In a second version, the motor is controlled to supply a predetermined amount of nutation motion to a body undergoing testing on a spin table for energy dissipation evaluation. In each version, the use of an angular accelerometer rather than a linear accelerometer or gyro to monitor nutation enables placement of the nutation control apparatus at any location relative to the spin axis of the body requiring only crude orientation and no calibration.

Hoffman, H. C.↗

NASA NTRS1986

The effects of mantle and anelasticity on nutations, earth tides, and tidal variations in rotation rate

The paper models the effects of mantle anelasticity on luni-solar nutations, on tidal deformation, on tidal variations in rotation rate, and on the eigenfrequency of the free core nutation. The results can be used to invert observations to solve for the anelastic contributions to the shear and bulk moduli of the upper and lower mantle. Specific anelastic models are used to numerically estimate the effects of anelasticity on these geodetic observables. The nutation estimates are compared with observational results. Among the conclusions: (1) mantle anelasticity is likely to be the most important source of damping for the free core nutation; (2) present VLBI nutation results are, in principle, accurate enough to usefully bound anelasticity at diurnal periods. But the discrepancy between the VLBI observed nutations and the 1984 IAU nutation model cannot be explained by anelasticity and is not yet well enough understood to allow anelasticity to be determined from the data.

Wahr, John↗

NASA NTRS1972

Design analysis for a nutating plate drive 4

A simplified design analysis was conducted on a nutating plate type drive system for a 2500 horsepower helicopter main rotor gear box. A drive system that split the output torque evenly between two nutating plates for the purpose of reducing the load on each nutating plate was analyzed. Needle bearings were used on the nutating plate pins. The results of the analysis indicate that the required load capacity of the pin bearings and the speed of the nutating plate bearings were beyond the state-of-the-art capacity of rolling-element bearings. The analysis further indicates that the nutating plate drive is less efficient, and results in a higher weight per horsepower than a conventional planetary helicopter transmission with similar design specifications.

Loewenthal, S. H.↗

NASA NTRS1977

Effects of increased gravity force on nutations of sunflower hypocotyls

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.

Brown, A. H.↗

NASA NTRS1983

Method of damping nutation motion with minimum spin axis attitude disturbance

In a method of and apparatus for damping nutation of a spinning spacecraft, spin axis attitude disturbances are substantially reduced by controlling at least one nutation damping gas thruster to fire with nonuniform gas pulses. During the beginning of a nutation control sequence, the duration of successive gas pulses is gradually increased (up pulsed) from zero to a predetermined maximum duration. The duration of successive pulses is then maintained constant for a time period. Finally, at the end of the nutation control sequence, the duration of successive gas pulses is gradually reduced to zero (down pulsed). Up pulsing of the gas thruster is initiated in response to a predetermined maximum nutation angle measured by an accelerometer. Down pulsing of the thruster is initiated in response to a predetermined minimum nutation angle.

Hoffman, H. C.↗

NASA NTRS1986

Geodesy by radio interferometry: Studies of the forced nutations of the earth. I - Data analysis. II - Interpretation

Very long baseline interferometry (VLBI) observations of compact extragalactic radio sources collected in North America and Europe between July 1980-December 1984 are analyzed. The nutations derived from VLBI data are compared with the nutations in the Wahr series (1981). Good correlation of the data is observed; however, it is detected that a correction of -1.80 + or - 0.18-i(0.42 + or - 0.18) is required for the amplitude of the retrograde annual nutation in the Wahr series. The change in free core nutation resonance frequency is calculated to explain the derivation in the retrograde annual nutation. It is concluded that VLBI earth nutation measurements have sufficient accuracy to be sensitive to core-mantle boundary properties.

Herring, T. A.↗

NASA NTRS1990

The earth's forced nutations - Geophysical implications

Theories of nutation are examined critically to develop an extension of the theoretical description based on an earth in nonhydrostatic equilibrium. The estimation of nutation amplitude as a function of frequency is reviewed with reference to contributing variables such as the oceans, mantle anelasticity, and nonhydrostatic structure. Theoretical results by Wahr (1981) are compared to those of VLBI observations, and other VLBI data are used to discuss Wahr and Bergen's (1986) theoretical nutation admittances for an anelastic earth. The contributions associated with the tilt-over mode and with free-core nutations (FCN) are discussed, and the contribution of anelasticity is examined. The VLBI data show that nutation data are important sources of information regarding the earth's interior. Nutation amplitudes are derived with a model for a nonhydrostatically prestressed earth to determine the FCN contributions.

Wahr, J. M.↗

NASA NTRS1994

Contributions to the Earth's obliquity rate, precession, and nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The J(sub2) effects have generally been allowed for in past nutation theories and some procession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta phi plus out-of-phase contributions of 0.14 mas in Delta phi and -0.03 mas in Delta epsilon. The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C = 0.003 273 763 4 which, in combination with a satellite-derived J(sub2), gives a normalized polar moment of inertia C/MR(exp2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub2). Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗

NASA NTRS1994

Contributions to the Earth's Obliquity Rate, Precession, and Nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub 2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024 sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The effects have generally been allowed for in past nutation theories and some precession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta(psi) plus out-of-phase contributions of 0.14 mas in Delta(psi) and -0.03 mas in Delta(sub epsilon). The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C =0.003 273 763 4 which, in combination with a satellite-derived J(sub 2), gives a normalized polar moment of inertia C/MR(exp 2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub 2) Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗

NASA NTRS1997

Interaction of light and gravitropism with nutation of hypocotyls of Arabidopsis thaliana seedlings

Etiolated seedlings of Arabidopsis thaliana nutated under conditions of physiological darkness while about ten percent of monitored individuals exhibited regular elliptical nutation, circumnutation. Pre-irradiation with red light prevented occurrence of circumnutation without having an effect on the average rate of the nutational movement. Phototropic response of seedlings to unilateral blue light appeared to be superimposed over nutation. Throughout gravitropism, some seedlings continued to exhibit nutation suggesting that these two processes are independently controlled. Based on these results, we suggest that nutation in Arabidopsis probably is not controlled by the mechanism predicted by the theory of gravitropic overshoots.

NASA Discipline Plant Biology↗

NASA NTRS1971

Introduction to passive nutation dampers

Coning motion can prevent photographic and TV cameras and other oriented spacecraft experiments from maintaining a steady scan, and it can introduce a ripple in the high-gain communication system. Nutation dampers are used to remove this type of spacecraft instability. The first nutation damper flown in a missile for the stabilization of the gyroscope consisted of a hollow ring that was partially filled with mercury, and the sloshing of the mercury dissipated the nutational energy. A similar mercury-ring damper was used in the Pioneer 1 lunar probe in 1958 and became the first nutation damper to be used in space. Since then many types of nutation dampers have been designed for spin-stabilized spacecraft ranging in size from small scientific satellites to large space stations.

Herzl, G. C.↗

NASA NTRS1973

Nutation control during precession of a spin-stabilized spacecraft

The effects of precession thrust pulses and energy dissipation upon nutation of a spin-stabilized spacecraft are studied. Methods for controlling nutation during a precession maneuver are proposed and examined. A precession modulation control law is developed which uses precession thrust pulses to control nutation. Digital simulations show that precession control with separate nutation control is the fastest precessing system; however, the precession modulation method is only fractionally slower while not requiring a separate nutation control system.

Taylor, J. M.↗

NASA NTRS1974

Nutation control during precession of a spin-stabilized spacecraft

Precession maneuver control laws for single-spin spacecraft are investigated so that nutation is concurrently controlled. Analysis has led to the development of two types of control laws employing precession modulation for concurrent nutation control. Results were verified through digital simulation of a Synchronous Meteorological Satellite (SMS) configuration. An addition research effort was undertaken to investigate the cause and elimination of nutation anomalies in dual-spin spacecraft. A literature search was conducted and a dual-spin configuration was simulated to verify that nutational anomalies are not predicted by the existing nonlinear model. No conclusions were drawn as to the cause of the observed nutational anomalies in dual-spin spacecraft.

Source record↗

NASA NTRS1988

VLBI studies of the nutations of the earth

The analysis of six years of VLBI data has yielded corrections to the coefficients of the seven largest terms in the IAU 1980 nutation series with periods of one year or less, with accuracies approaching the truncation error of this nutation series (0.1 mas). This paper examines the methods used to extract the nutation information from the VLBI data, the calculation of the uncertanties of the resultant corrections to the nutation-series coefficients, and current research on the earth's nutations.

Herring, T. A.↗