The Earth’s Free Core Nutation(FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects.High-precision superconducting gravimeter(SG) and very long baseline interfe...The Earth’s Free Core Nutation(FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects.High-precision superconducting gravimeter(SG) and very long baseline interferometry(VLBI) provide good observation techniques for detecting the FCN parameters.However,some choices in data processing and solution procedures increase the uncertainty of the FCN parameters.In this study,we analyzed the differences and the effectiveness of weight function and ocean tide corrections in the FCN parameter detection using synthetic data,SG data from thirty-one stations,and the 10 celestial pole offset(CPO) series.The results show that significant discrepancies are caused by different computing options for a single SG station.The stacking method,which results in a variation of0.24-5 sidereal days(SDs) in the FCN period(T) and 10^(3)-10^(4) in the quality factor(Q) due to the selection of the weighting function and the ocean tide model(OTM),can effectively suppress this influence.The statistical analysis results of synthetic data shows that although different weight choices,while adjusting the proportion of diurnal tidal waves involved,do not significantly improve the accuracy of fitted FCN parameters from gravity observations.The study evaluated a series of OTMs using the loading correction efficiency.The fitting of FCN parameters can be improved by selecting the mean of appropriate OTMs based on the evaluation results.Through the estimation of the FCN parameters based on the forced nutation,it was found that the weight function P_(1) is more suitable than others,and different CPO series(after 2009) resulted in a difference of 0.4 SDs in the T and of 103 in the Q.We estimated the FCN parameters for SG(T=430.4±1.5 SDs and Q=1.52×10^(4)±2.5×10^(3)) and for VLBI(T=429.8±0.7 SDs,Q=1.88×10^(4)±2.1×10^(3)).展开更多
Based on the nearly diurnal resonance in the tidal gravity observations, the temporal variations in period of the Earth＇s free core nutation （FCN） are investigated by using the tidal gravity observations of 18-year...Based on the nearly diurnal resonance in the tidal gravity observations, the temporal variations in period of the Earth＇s free core nutation （FCN） are investigated by using the tidal gravity observations of 18-year duration recorded continu- ously with a superconducting gravimeter （SG） at Brussels. The effects of the global oceanic tide loading and local barometric pressure on the SG observations have been removed by using eleven high-precision global digital models of oceanic tides and barometric pressure measurements recorded simultaneously at the same site. The results indicate that there exist decade-scale variations in the FCN period. The results should be further confirmed by the measurements using other space-based geodetic techniques （such as the very long baseline interferometry） and the SG observations from globally distributed stations.展开更多
Vortices motion in the anisotropic turbulent flow of cyclones makes a vital impact on flow stability and collection performance.Nevertheless,there remains a lack of clarity in the overall feature of vortices motion.In...Vortices motion in the anisotropic turbulent flow of cyclones makes a vital impact on flow stability and collection performance.Nevertheless,there remains a lack of clarity in the overall feature of vortices motion.In this work,a numerical analysis was conducted to clarify the complex motion of the vortex core in a cyclone separator.The validity of the numerical model was demonstrated by comparing the computational results with experimental data in the literature.As revealed by the results,the vortex core not only has a precession motion about the geometrical center axis but also does a nutation motion in the axial direction.The frequencies of the precession motions show two main peaks.And the magnitudes of the precession and nutation motions have non-uniform distributions in the cyclone.Moreover,the precession-nutation motions of the vortex cores exhibit a similar fluctuant pattern to the dust ring on the separator wall.The inlet gas velocity and the inlet solid loading show vital effects on the magnitudes and frequencies of precession and nutation motion.展开更多
We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double cir...We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double circular arc tooth profile and based on the equal tooth strength principle. The nutation drive meshing coordinate system was set up by introducing the cone vertex error, tilt error, nutation angle error and spiral angle error. The tooth profile equations of the double circular arc external and internal spiral bevel gears were further obtained based on the crown gear tooth profile equation concerning above mentioned error parameters. The influences of the nutation gear reducer tooth contact conditions were analyzed with the gear tilt error and axial misalignment error. Finally, the correctness of the theoretical analysis was verified by the contact spot test.展开更多
A nonlinear mathematic model taking the nutation and precession angles as variables for the coning motion of projectile was established according to a short period moment projection of the spining projectile. By intro...A nonlinear mathematic model taking the nutation and precession angles as variables for the coning motion of projectile was established according to a short period moment projection of the spining projectile. By introducing the generalized nutation angle and precession angular speed, the model that is difficult to be resolved can be transformed to a resolvable one. The interrelationship between nutation and precession was analyzed based on the linear model, and the stability condition was obtained for the spinning projectile. For the nonlinear model, the effects of the nutation and precession on the limit circle of the projectile's coning motion were investigated, and the analytical relations between the nutation angle and the precession angular speed in the steady coning motion of the spinning projectile were given.展开更多
The Earth＇s free core nutation （FCN） is a retrograde eigenrnode which is attributed to the interaction between the solid mantle and the liquid core of the rotational elliptical Earth. This mode appears as an eigenm...The Earth＇s free core nutation （FCN） is a retrograde eigenrnode which is attributed to the interaction between the solid mantle and the liquid core of the rotational elliptical Earth. This mode appears as an eigenmode of nearly diurnal free wobble （NDFW） in a terrestrial reference frame with a period of about one day （XU et al, 2001）. Therefore, the NDFW will lead to an obvious resonance enhancement in the diurnal tidal gravity observations, especially those of the tidal waves with frequencies closed to its eigenfrequency such as P1, K1, ψ1 and Ф1. The FCN resonance parameters can be retrieved accurately by high-precision tidal gravity observations, especially those recorded with the superconducting gravimeters （SG）. The Global Geodynamics Project （GGP） organized by IUGG took it as an important content for determining the FCN resonance parameters by using gravity data. However, the results are affected by many factors such as station location, background noise, the selection of the tide-generating potential tables, ocean tide models, data processing techniques and so on. In our study, the FCN parameters will be retrieved by using the SG observations at Wuhan, and the effects of the choices of various tide-generating potential tables, oceanic models and weight functions on the estimation of the FCN parameters will be discussed in detail,展开更多
The rotation of the Earth's liquid core creates the Nearly Diurnal Free Wobble (NDFW). It is one of the problems of researching the Earth's liquid core for us to retrieve the parameters of the Earth's Free...The rotation of the Earth's liquid core creates the Nearly Diurnal Free Wobble (NDFW). It is one of the problems of researching the Earth's liquid core for us to retrieve the parameters of the Earth's Free Core Nutation (FCN),from the Earth's liquid core resonance of gravity tide waves on the diurnal frequency band. Since 1987, some scientists in many different countries have come to calculate the parameters of FCN by using the observational data of gravity tide waves on the diumal frequency band. They basically followed the Stacking method, which needed five diurnal waves for the resolution. In this paper, authors introduced the Aky-Btk value method with clearly geometrical meaning as a new method, which only requires three very high signal-noise-ratio waves o1, K1 and P1 for the resolution. Authors chose the observational data of the three superconducting gravimeter stations respectively located in Cantley of Canada, Wuhan of China and Brussels of Belgium, to compute the parameters of FCN. It was the first time that the observational results of the parameters of FCN obtained from gravitational tide were in accord with the parameters of FCN gained from VLBI since 1987.展开更多
Seismic observations shows that the inner core rotates faster than the mantle and the rotation axis of the inner core may not align with the rotation axis of the mantle. Free core nutation reflects core's informat...Seismic observations shows that the inner core rotates faster than the mantle and the rotation axis of the inner core may not align with the rotation axis of the mantle. Free core nutation reflects core's information. We discuss the effect of the inner core's differential rotation on free core nutation from two aspects: rotation speed and deflection angle. Our result shows it is in accordance with the observations when the inner core's rotation speed doesn't exceed 10° faster than mantle's per year, and the deflection angle is less than 1°,if the rotation speed and the deflection angle are respectively considered separately.展开更多
The theory of Smith (1977,1980) is generalized to include both forced and free rotations by introducing an arbitrarily rotating nutation frame.The Eulerien equations are transformed to include the following unknowns:t...The theory of Smith (1977,1980) is generalized to include both forced and free rotations by introducing an arbitrarily rotating nutation frame.The Eulerien equations are transformed to include the following unknowns:the angular velocity of the nutation frame with respect to the spatial frame,which represents the nutation,and the angles defining the orientation of the Earth with respect to the nutation frame,which represents the polar motion.Together with the definition of the nutation frame (as the definition of the nutation frame is arbitrary to some extent),one can solve simultaneously forced and free nutation and polar motion.As demonstrative examples,studies of nutation and polar motion are made by assuming the nutation axis to be the Earth’s figure axis,rotation axis and angular momentum axis respectively.And the case of the celestial ephemeris pole is also studied.展开更多
The rotation of the physical Earth not only obeys the law of conservation of angular momentum but follows also the three-finger rule of the right-handed system. The reference frame in the Earth is most essential. The ...The rotation of the physical Earth not only obeys the law of conservation of angular momentum but follows also the three-finger rule of the right-handed system. The reference frame in the Earth is most essential. The generalized Eulerian equation of motion or the Liouville equation is to represent global geodynamics in general, which is examined directly through the observation of the Earth’s rotation and surface motions, with no additional assumptions after fundamental physics. Rotational acceleration, polar motion, plate tectonics, and seismicity observed on the Earth’s surface indicate that the Earth’s angular momentum is perturbed and adjusting independently of external torques. (For more information,please refer to the PDF.)展开更多
In this review paper, we examine the changes in the Earth orientation in space and focus on the nutation（shorter-term periodic variations）, which is superimposed on precession（long-term trend on a timescale of year...In this review paper, we examine the changes in the Earth orientation in space and focus on the nutation（shorter-term periodic variations）, which is superimposed on precession（long-term trend on a timescale of years）. We review the nutation modelling involving several coupling mechanisms at the core-mantle boundary using the Liouville angular momentum equations for a two-layered Earth with a liquid flattened core. The classical approach considers a Poincare fluid for the core with an inertial pressure coupling mechanism at the core-mantle boundary. We examine possible additional coupling mechanisms to explain the observations. In particular, we examine how we can determine the flattening of the core as well as information on the magnetic field and the core flow from the nutation observations. The precision of the observations is shown to be high enough to increase our understanding on the coupling mechanisms at the core-mantle boundary.展开更多
For the motion of a sphere on a rough horizontal plane, in the previous paper[1]the author aimed at providing approximate analytical solutions while the nutation is neglected,In this paper ,the control equations for t...For the motion of a sphere on a rough horizontal plane, in the previous paper[1]the author aimed at providing approximate analytical solutions while the nutation is neglected,In this paper ,the control equations for the sphere with nutation have beendeduced on the basis of paper [1]. Through the medium of solving these equations,the conclusion for the velocity of contact point in paper [1]is still proved true for the case with nutation.What is more ,some interesting results are gained ,for example the ve-locity of centre and contact point is relative to the angular velocity of spin and nuta-tion the direction of velocity of centre and contact point is constant.Under the condi-tion which is supposed to be weak nutation,the approximate analytical solutions are obtained,so that the results of paper [1]is proved to be true.展开更多
By stacking high-precision tidal gravity observations obtained with superconducting gravimeters at six stations in China, Japan, Belgium, France, Germany and Finland, the local systematical discrepancies in the parame...By stacking high-precision tidal gravity observations obtained with superconducting gravimeters at six stations in China, Japan, Belgium, France, Germany and Finland, the local systematical discrepancies in the parameter fitting, caused by atmospheric, oceanic tidal loading and the other local environmental perturbations, are eliminated effectively. As a result, the resonance parameters of the Earth's free core nutation are accurately determined. In this study, the eigenperiod of free core nutation is given as 429.0 sidereal days, which is in agreement with those published in the previous studies. It is about 30 sidereal days less than those calculated in theoretical models (about 460 sidereal days), which confirms the real ellipticity of the fluid core of the Earth to be about 5% larger than the one expected in assumption of hydrostatic equilibrium. The quality factor (Q value) of free core nutation is given as about 9543, which, compared with those determined before based on the body tide observations, is much larger, but more close to those obtained using the VLBI observations. The complex resonance strength is also determined as (?6.10(10?4, ?0.01(10?4)(/h, which can principally describe the deformation characteristics of an anelastic mantle.展开更多
The variation of mass, and moment of inertia of a spin-stabilized spacecraft leads to concern about the nutation instability. Here a careful analysis on the nutation instability is performed on a spacecraft propelled ...The variation of mass, and moment of inertia of a spin-stabilized spacecraft leads to concern about the nutation instability. Here a careful analysis on the nutation instability is performed on a spacecraft propelled by solid rocket booster（SRB）. The influences of specific solid propellant designs on transversal angular velocity are discussed. The results show that the typical SRB of End Burn suppresses the non-principal axial angular velocity. On the contrary, the frequently used SRB of Radial Burn could amplify the transversal angular velocity. The nutation instability caused by a design of Radial Burn could be remedied by the addition of End Burn at the same time based on the study of the combination design of both End Burn and Radial Burn.The analysis of the results proposes the design conception of how to control the nutation motion.The method is suitable to resolve the nutation instability of solid rocket motor with complex propellant patterns.展开更多
Detumbling operation toward a rotating target with nutation is meaningful for debris removal but challenging. In this study, a deformable end-effector is first designed based on the requirements for contacting the nut...Detumbling operation toward a rotating target with nutation is meaningful for debris removal but challenging. In this study, a deformable end-effector is first designed based on the requirements for contacting the nutating target. A dual-arm robotic system installed with the deformable end-effectors is modeled and the movement of the end-tips is analyzed. The complex operation of the contact toward a nutating target places strict requirements on control accuracy and controller robustness. Thus, an improvement of the tracking error transformation is proposed and an adaptive sliding mode controller with prescribed performance is designed to guarantee the fast and precise motion of the effector during the contact detumbling.Finally, by employing the proposed effector and the controller,numerical simulations are carried out to verify the effectiveness and efficiency of the contact detumbling toward a nutating target.展开更多
The location of charge-balancing sodium cations plays an important role in determining the adsorption and catalytic properties of zeolites.Solid-state <sup>23</sup>Na nuclear magnetic resonance （NMR） can...The location of charge-balancing sodium cations plays an important role in determining the adsorption and catalytic properties of zeolites.Solid-state <sup>23</sup>Na nuclear magnetic resonance （NMR） can provide information about the distribution and chemical surroundings of sodium cations in zeolites.A number of papers have been published using various <sup>23</sup>Na NMR techniques to investigate the distribution of sodium cations and their interactions with water molecules in hydrated zeolite A, zeolite Y and sodalites.In addition, Challoner et al. have studied the motion of展开更多
The influences of nutation trail accuracy,simplification of coupling model,spot position jitter,and power variation of incident light on the detection error are analyzed theoretically.Under the condition of satisfying...The influences of nutation trail accuracy,simplification of coupling model,spot position jitter,and power variation of incident light on the detection error are analyzed theoretically.Under the condition of satisfying the requirements,the nutation radius is less than 1.13μm,the accuracy of the nutation trail is less than 0.04μm,and the detection range is[?5μm,+5μm].The nutation frequency is 160 times spot position jitter frequency and 100 times intensity jitter frequency of incident light.The analysis is of great significance for determining nutation radius and frequency in the tracking system based on fiber nutation.展开更多
In the aspect of examination by observations and based on a longer data span and improved precision of very_long baseline interferometry observations, the corrections to the IAU 1976 precession constant and the coeffi...In the aspect of examination by observations and based on a longer data span and improved precision of very_long baseline interferometry observations, the corrections to the IAU 1976 precession constant and the coefficients of IAU 1980 nutation series are solved. The corrections to coefficients of long periodic terms, the detection of the retrograde free core nutation, and the possible relation between the corrections to coefficients of the prograde annual term and the enviromental temperature are also briefly discussed.展开更多
It is well known that a variation in the direction of Earth’s rotation axis is a real astronomical phenomenon, named nutation. It is interesting if a variation of this axis can take place only in intensity, in the si...It is well known that a variation in the direction of Earth’s rotation axis is a real astronomical phenomenon, named nutation. It is interesting if a variation of this axis can take place only in intensity, in the simplest theoretical case of only two rigid body dynamics. This paper presents two positions of the Moon during its monthly orbit, where a sudden variation of Earth’s rotation axis in intensity can take place. The duration of this phenomenon is limited in time, maybe an instant or a day, and then a vortex can appear.展开更多
Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied. The dynamic equations are derived by conserva- tion of angular momentum and force equilibrium principl...Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied. The dynamic equations are derived by conserva- tion of angular momentum and force equilibrium principle. A feedback control strategy of the momentum wheel is ap- plied for the attitude maneuver. The residual nutation of the spacecraft in maneuver process changes with some chosen parameters, such as steady state time, locations of the liq- uid container and the appendage, and appendage parame- ters. The results indicate that locations in the second and fourth quadrants of the body-fixed coordinate system and the second quadrant of the wall of the main body are better choices for.placing the liquid containers and the appendage than other locations if they can be placed randomly. Higher density and thicker cross section are better for lowering the residual nutation if they can be changed. Light appendage can be modeled as a rigid body, which results in a larger residual nutation than a flexible model though. The resid- ual nutation decreases with increasing absolute value of the initial sloshing angular height.展开更多
基金supported by the Open Fund of Hubei Luojia Laboratory (No. 220100033)the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB41000000)+1 种基金National Natural Science Foundation of China (Grant Nos. 42174108, 41874094, 42192535 and 42242015)the Young Top-notch Talent Cultivation Program of Hubei Province。
文摘The Earth’s Free Core Nutation(FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects.High-precision superconducting gravimeter(SG) and very long baseline interferometry(VLBI) provide good observation techniques for detecting the FCN parameters.However,some choices in data processing and solution procedures increase the uncertainty of the FCN parameters.In this study,we analyzed the differences and the effectiveness of weight function and ocean tide corrections in the FCN parameter detection using synthetic data,SG data from thirty-one stations,and the 10 celestial pole offset(CPO) series.The results show that significant discrepancies are caused by different computing options for a single SG station.The stacking method,which results in a variation of0.24-5 sidereal days(SDs) in the FCN period(T) and 10^(3)-10^(4) in the quality factor(Q) due to the selection of the weighting function and the ocean tide model(OTM),can effectively suppress this influence.The statistical analysis results of synthetic data shows that although different weight choices,while adjusting the proportion of diurnal tidal waves involved,do not significantly improve the accuracy of fitted FCN parameters from gravity observations.The study evaluated a series of OTMs using the loading correction efficiency.The fitting of FCN parameters can be improved by selecting the mean of appropriate OTMs based on the evaluation results.Through the estimation of the FCN parameters based on the forced nutation,it was found that the weight function P_(1) is more suitable than others,and different CPO series(after 2009) resulted in a difference of 0.4 SDs in the T and of 103 in the Q.We estimated the FCN parameters for SG(T=430.4±1.5 SDs and Q=1.52×10^(4)±2.5×10^(3)) and for VLBI(T=429.8±0.7 SDs,Q=1.88×10^(4)±2.1×10^(3)).
基金supported by the Key Project of the Knowledge Innovation of Chinese Academy of Sciences (Grant No. KZCX2-YW-133, KZCX2-YW-Q08-2)National Natural Science Foun-dation of China (Grant No. 40874038 and 40730316)
文摘Based on the nearly diurnal resonance in the tidal gravity observations, the temporal variations in period of the Earth＇s free core nutation （FCN） are investigated by using the tidal gravity observations of 18-year duration recorded continu- ously with a superconducting gravimeter （SG） at Brussels. The effects of the global oceanic tide loading and local barometric pressure on the SG observations have been removed by using eleven high-precision global digital models of oceanic tides and barometric pressure measurements recorded simultaneously at the same site. The results indicate that there exist decade-scale variations in the FCN period. The results should be further confirmed by the measurements using other space-based geodetic techniques （such as the very long baseline interferometry） and the SG observations from globally distributed stations.
基金Authors thank for the joint funding of a Key Research and Development Plan of Shandong Province(Public Science and Technology)(2019GSF109038)the Key Laboratory of Multiphase Flow Reaction and Separation Engineering of Shandong Province(2019MFRSE-A01)the National Natural Science Foundation of China(51809236).
文摘Vortices motion in the anisotropic turbulent flow of cyclones makes a vital impact on flow stability and collection performance.Nevertheless,there remains a lack of clarity in the overall feature of vortices motion.In this work,a numerical analysis was conducted to clarify the complex motion of the vortex core in a cyclone separator.The validity of the numerical model was demonstrated by comparing the computational results with experimental data in the literature.As revealed by the results,the vortex core not only has a precession motion about the geometrical center axis but also does a nutation motion in the axial direction.The frequencies of the precession motions show two main peaks.And the magnitudes of the precession and nutation motions have non-uniform distributions in the cyclone.Moreover,the precession-nutation motions of the vortex cores exhibit a similar fluctuant pattern to the dust ring on the separator wall.The inlet gas velocity and the inlet solid loading show vital effects on the magnitudes and frequencies of precession and nutation motion.
基金Funded by the National Natural Science Foundation of China(Grant No.51275092)the Program of Fujian Provincial Industrial Robot Basic Components Technology Research and Development Center(Grant No.2014H21010011)the Program of Fujian Provincial Collaborative Innovation Center for High-end Equipment Manufacturing
文摘We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double circular arc tooth profile and based on the equal tooth strength principle. The nutation drive meshing coordinate system was set up by introducing the cone vertex error, tilt error, nutation angle error and spiral angle error. The tooth profile equations of the double circular arc external and internal spiral bevel gears were further obtained based on the crown gear tooth profile equation concerning above mentioned error parameters. The influences of the nutation gear reducer tooth contact conditions were analyzed with the gear tilt error and axial misalignment error. Finally, the correctness of the theoretical analysis was verified by the contact spot test.
基金Sponsored by the National Science Foundation of China (10972034)
文摘A nonlinear mathematic model taking the nutation and precession angles as variables for the coning motion of projectile was established according to a short period moment projection of the spining projectile. By introducing the generalized nutation angle and precession angular speed, the model that is difficult to be resolved can be transformed to a resolvable one. The interrelationship between nutation and precession was analyzed based on the linear model, and the stability condition was obtained for the spinning projectile. For the nonlinear model, the effects of the nutation and precession on the limit circle of the projectile's coning motion were investigated, and the analytical relations between the nutation angle and the precession angular speed in the steady coning motion of the spinning projectile were given.
基金The Knowledge Innovation Project of Chinese Academy of Sciences (KZCX2-YW-133)National Natural Science Foundation of China (40574034 and 40730316).
文摘The Earth＇s free core nutation （FCN） is a retrograde eigenrnode which is attributed to the interaction between the solid mantle and the liquid core of the rotational elliptical Earth. This mode appears as an eigenmode of nearly diurnal free wobble （NDFW） in a terrestrial reference frame with a period of about one day （XU et al, 2001）. Therefore, the NDFW will lead to an obvious resonance enhancement in the diurnal tidal gravity observations, especially those of the tidal waves with frequencies closed to its eigenfrequency such as P1, K1, ψ1 and Ф1. The FCN resonance parameters can be retrieved accurately by high-precision tidal gravity observations, especially those recorded with the superconducting gravimeters （SG）. The Global Geodynamics Project （GGP） organized by IUGG took it as an important content for determining the FCN resonance parameters by using gravity data. However, the results are affected by many factors such as station location, background noise, the selection of the tide-generating potential tables, ocean tide models, data processing techniques and so on. In our study, the FCN parameters will be retrieved by using the SG observations at Wuhan, and the effects of the choices of various tide-generating potential tables, oceanic models and weight functions on the estimation of the FCN parameters will be discussed in detail,
文摘The rotation of the Earth's liquid core creates the Nearly Diurnal Free Wobble (NDFW). It is one of the problems of researching the Earth's liquid core for us to retrieve the parameters of the Earth's Free Core Nutation (FCN),from the Earth's liquid core resonance of gravity tide waves on the diurnal frequency band. Since 1987, some scientists in many different countries have come to calculate the parameters of FCN by using the observational data of gravity tide waves on the diumal frequency band. They basically followed the Stacking method, which needed five diurnal waves for the resolution. In this paper, authors introduced the Aky-Btk value method with clearly geometrical meaning as a new method, which only requires three very high signal-noise-ratio waves o1, K1 and P1 for the resolution. Authors chose the observational data of the three superconducting gravimeter stations respectively located in Cantley of Canada, Wuhan of China and Brussels of Belgium, to compute the parameters of FCN. It was the first time that the observational results of the parameters of FCN obtained from gravitational tide were in accord with the parameters of FCN gained from VLBI since 1987.
基金supported by the National Natural Science Foundation of China (11373058/11773058/10903023/11133004)the CAS Key Lab of Planetary Science
文摘Seismic observations shows that the inner core rotates faster than the mantle and the rotation axis of the inner core may not align with the rotation axis of the mantle. Free core nutation reflects core's information. We discuss the effect of the inner core's differential rotation on free core nutation from two aspects: rotation speed and deflection angle. Our result shows it is in accordance with the observations when the inner core's rotation speed doesn't exceed 10° faster than mantle's per year, and the deflection angle is less than 1°,if the rotation speed and the deflection angle are respectively considered separately.
基金ProjectsupportedbytheNationalNaturalScienceFoundationofChi na (No .498740 0 3)
文摘The theory of Smith (1977,1980) is generalized to include both forced and free rotations by introducing an arbitrarily rotating nutation frame.The Eulerien equations are transformed to include the following unknowns:the angular velocity of the nutation frame with respect to the spatial frame,which represents the nutation,and the angles defining the orientation of the Earth with respect to the nutation frame,which represents the polar motion.Together with the definition of the nutation frame (as the definition of the nutation frame is arbitrary to some extent),one can solve simultaneously forced and free nutation and polar motion.As demonstrative examples,studies of nutation and polar motion are made by assuming the nutation axis to be the Earth’s figure axis,rotation axis and angular momentum axis respectively.And the case of the celestial ephemeris pole is also studied.
文摘The rotation of the physical Earth not only obeys the law of conservation of angular momentum but follows also the three-finger rule of the right-handed system. The reference frame in the Earth is most essential. The generalized Eulerian equation of motion or the Liouville equation is to represent global geodynamics in general, which is examined directly through the observation of the Earth’s rotation and surface motions, with no additional assumptions after fundamental physics. Rotational acceleration, polar motion, plate tectonics, and seismicity observed on the Earth’s surface indicate that the Earth’s angular momentum is perturbed and adjusting independently of external torques. (For more information,please refer to the PDF.)
基金funding from the European Research Council under ERC Advanced Grant 670874
文摘In this review paper, we examine the changes in the Earth orientation in space and focus on the nutation（shorter-term periodic variations）, which is superimposed on precession（long-term trend on a timescale of years）. We review the nutation modelling involving several coupling mechanisms at the core-mantle boundary using the Liouville angular momentum equations for a two-layered Earth with a liquid flattened core. The classical approach considers a Poincare fluid for the core with an inertial pressure coupling mechanism at the core-mantle boundary. We examine possible additional coupling mechanisms to explain the observations. In particular, we examine how we can determine the flattening of the core as well as information on the magnetic field and the core flow from the nutation observations. The precision of the observations is shown to be high enough to increase our understanding on the coupling mechanisms at the core-mantle boundary.
文摘For the motion of a sphere on a rough horizontal plane, in the previous paper[1]the author aimed at providing approximate analytical solutions while the nutation is neglected,In this paper ,the control equations for the sphere with nutation have beendeduced on the basis of paper [1]. Through the medium of solving these equations,the conclusion for the velocity of contact point in paper [1]is still proved true for the case with nutation.What is more ,some interesting results are gained ,for example the ve-locity of centre and contact point is relative to the angular velocity of spin and nuta-tion the direction of velocity of centre and contact point is constant.Under the condi-tion which is supposed to be weak nutation,the approximate analytical solutions are obtained,so that the results of paper [1]is proved to be true.
基金This work is supported jointly by the Chinese Academy of Sciences (Grant Nos. KZCX2-106 and KZ952-J1 -411) the National Natural Science Foundation of China (Grant Nos. 49925411 and 40174022).
文摘By stacking high-precision tidal gravity observations obtained with superconducting gravimeters at six stations in China, Japan, Belgium, France, Germany and Finland, the local systematical discrepancies in the parameter fitting, caused by atmospheric, oceanic tidal loading and the other local environmental perturbations, are eliminated effectively. As a result, the resonance parameters of the Earth's free core nutation are accurately determined. In this study, the eigenperiod of free core nutation is given as 429.0 sidereal days, which is in agreement with those published in the previous studies. It is about 30 sidereal days less than those calculated in theoretical models (about 460 sidereal days), which confirms the real ellipticity of the fluid core of the Earth to be about 5% larger than the one expected in assumption of hydrostatic equilibrium. The quality factor (Q value) of free core nutation is given as about 9543, which, compared with those determined before based on the body tide observations, is much larger, but more close to those obtained using the VLBI observations. The complex resonance strength is also determined as (?6.10(10?4, ?0.01(10?4)(/h, which can principally describe the deformation characteristics of an anelastic mantle.
基金supported by the National Natural Science Foundation of China (Nos. 11502086 and 11502087)
文摘The variation of mass, and moment of inertia of a spin-stabilized spacecraft leads to concern about the nutation instability. Here a careful analysis on the nutation instability is performed on a spacecraft propelled by solid rocket booster（SRB）. The influences of specific solid propellant designs on transversal angular velocity are discussed. The results show that the typical SRB of End Burn suppresses the non-principal axial angular velocity. On the contrary, the frequently used SRB of Radial Burn could amplify the transversal angular velocity. The nutation instability caused by a design of Radial Burn could be remedied by the addition of End Burn at the same time based on the study of the combination design of both End Burn and Radial Burn.The analysis of the results proposes the design conception of how to control the nutation motion.The method is suitable to resolve the nutation instability of solid rocket motor with complex propellant patterns.
基金supported by the National Natural Science Foundation of China(11972077,11672035)。
文摘Detumbling operation toward a rotating target with nutation is meaningful for debris removal but challenging. In this study, a deformable end-effector is first designed based on the requirements for contacting the nutating target. A dual-arm robotic system installed with the deformable end-effectors is modeled and the movement of the end-tips is analyzed. The complex operation of the contact toward a nutating target places strict requirements on control accuracy and controller robustness. Thus, an improvement of the tracking error transformation is proposed and an adaptive sliding mode controller with prescribed performance is designed to guarantee the fast and precise motion of the effector during the contact detumbling.Finally, by employing the proposed effector and the controller,numerical simulations are carried out to verify the effectiveness and efficiency of the contact detumbling toward a nutating target.
基金Project supported by the National Natural Science Foundation of China.
文摘The location of charge-balancing sodium cations plays an important role in determining the adsorption and catalytic properties of zeolites.Solid-state <sup>23</sup>Na nuclear magnetic resonance （NMR） can provide information about the distribution and chemical surroundings of sodium cations in zeolites.A number of papers have been published using various <sup>23</sup>Na NMR techniques to investigate the distribution of sodium cations and their interactions with water molecules in hydrated zeolite A, zeolite Y and sodalites.In addition, Challoner et al. have studied the motion of
文摘The influences of nutation trail accuracy,simplification of coupling model,spot position jitter,and power variation of incident light on the detection error are analyzed theoretically.Under the condition of satisfying the requirements,the nutation radius is less than 1.13μm,the accuracy of the nutation trail is less than 0.04μm,and the detection range is[?5μm,+5μm].The nutation frequency is 160 times spot position jitter frequency and 100 times intensity jitter frequency of incident light.The analysis is of great significance for determining nutation radius and frequency in the tracking system based on fiber nutation.
文摘In the aspect of examination by observations and based on a longer data span and improved precision of very_long baseline interferometry observations, the corrections to the IAU 1976 precession constant and the coefficients of IAU 1980 nutation series are solved. The corrections to coefficients of long periodic terms, the detection of the retrograde free core nutation, and the possible relation between the corrections to coefficients of the prograde annual term and the enviromental temperature are also briefly discussed.
文摘It is well known that a variation in the direction of Earth’s rotation axis is a real astronomical phenomenon, named nutation. It is interesting if a variation of this axis can take place only in intensity, in the simplest theoretical case of only two rigid body dynamics. This paper presents two positions of the Moon during its monthly orbit, where a sudden variation of Earth’s rotation axis in intensity can take place. The duration of this phenomenon is limited in time, maybe an instant or a day, and then a vortex can appear.
基金supported by the National Natural Science Foundation of China (11072030)
文摘Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied. The dynamic equations are derived by conserva- tion of angular momentum and force equilibrium principle. A feedback control strategy of the momentum wheel is ap- plied for the attitude maneuver. The residual nutation of the spacecraft in maneuver process changes with some chosen parameters, such as steady state time, locations of the liq- uid container and the appendage, and appendage parame- ters. The results indicate that locations in the second and fourth quadrants of the body-fixed coordinate system and the second quadrant of the wall of the main body are better choices for.placing the liquid containers and the appendage than other locations if they can be placed randomly. Higher density and thicker cross section are better for lowering the residual nutation if they can be changed. Light appendage can be modeled as a rigid body, which results in a larger residual nutation than a flexible model though. The resid- ual nutation decreases with increasing absolute value of the initial sloshing angular height.
