Determining the moment of inertia of triaxial Mars with updated global gravity models

The principal moments of inertia(PMIs)with the principal axes are usually taken as the dynamic figure parameters of Mars;they can be deduced from satellite-observed degree-two gravitational potentials in recent global gravity models and from the dynamic ellipticities resulting from precession observations.These PMIs are natural and significant for the geodetic,geophysical,and geodynamic problems of Mars,which are functions of internal density distributions.In this study,a closed and concise formula for determining the PMIs of the entire planet and its core was developed based on the second invariants of gravity and a multipole expansion.We deduced the polar oblateness J^(2)and the equatorial ellipticity J_(22)of Mars to be 1.9566×10^(−3)and 6.3106×10^(−5),respectively.The preferred principal moments of inertia of Mars are A=2.66589×1036 kg·m^(2),B=2.66775×10^(36)kg·m^(2),and C=2.68125×10^(36)kg·m^(2).These values indicate that Mar is slightly triaxial.The equatorial principal moment of inertia of the Martian core is 1.46008×10^(35)kg·m^(2),accounting for~5.47%of the planet’s PMI;this result is critical for investigating the density and size of the core of Mars,and the planet’s free core nutation.

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

The principal moments of inertia calculated with the hydrostatic equilibrium figure of the Earth

As an indication of the Earth＇s mass distribution, the principal moments of inertia （PMOI, i.e., A, B, C） of the Earth are the basic parameters in studies of the global dynamics of the earth, like earth nutation, and the geophysics. From the aspect of observation, the PMOI can be calculated from the spherical coefficients of observed gravity field. In this paper, the PMOI are calculated directly according to its definition with the figures of the Earth＇s interior derived by a generalized theory of the hydrostatic equilibrium figure of the Earth. We obtain that the angle between the principal axis of the maximum moment of PMOI and the rotational axis is 0.184~, which means that the other two principal axes are very closely in the equatorial plane. Meanwhile, B-A is 1.60 x 10-5 MR2, and the global dynamical flattening （H） is calculated to be 3.29587 ~ 10-3, which is 0.67% different from the latest observation derived value Hobs（3.273795 × 10 ^-3） （Petit and Luzum, 2010）, and this is a significant improvement from the 1.1% difference between the value of H derived from traditional theories of the figure of the Earth and the value of Hobs. It shows that we can calculate the PMOI and H with an appropriate accuracy by a gener- alized theory of the hydrostatic equilibrium figure of the Earth.

THE CALCULATION METHOD OF FLYWHEEL MOMENT OFINERTIA OF CRANE MECHANISM

The origin and substance of the tlywheel moment calculation method of inertia mo ment of crane mechanism are set forth comprehensively and systematically in this paper, that is, the nucleus or the focus ofmoment of inertia calculation is the problem of calculating convertible tlywheelmoment. It is much better for the calculation of flywheel moment of loading move mass of lifting, traveling and rotating mechanism using the low of conservation of energy, the theorem of kinetic energyfor that of radius - changing mechanism, and the law of conservation of energy for that of all parts of gearing mechanism.

The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Motions in Complex Plane

In this paper, the Steiner area formula and the polar moments of inertia were expressed during one-parameter closed planar motions in complex plane. The Steiner points or Steiner normal concepts were described according to whe-ther rotation number was different from zero or equal to zero. The moving pole point was given with its components and its relation to the Steiner point or Steiner normal which was specified. The Steiner formula and the polar moments of inertia were expressed for the inverse motion. The fixed pole point was calculated for the inverse motion. The sagittal motion of a tele-scopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of the telescopic crane and its moving arm. The results obtained in the first section of this study were applied to this motion.

Theoretical and Practical Studies of Determining the Force of the Lifting-Lowering of the Roll Box

The lifting and lowering mechanism of the roll box of the saw gin, being an integral part of the ginning process, is used when starting the electric motor of the saw cylinder until its rated speed is reached to prevent an increase in the load current on it, as well as to start the ginning process. The article defines the kinematics of the movement, and also studies the regularity of the movement of the roll box of the saw gin when lifting it with the help of a pneumatic drive. The kinematics of the roll box movement was determined through experimental studies. Knowing the equation of motion, using the second-order Lagrange equation, the regularity of the change in the lifting force of the roll box was determined. Here the system is closed, its degree of freedom is equal to one. The angle of rotation of the roll box is taken as a generalized coordinate. Numerical results were obtained using the Matlab software environment. The theoretical analysis and graphs for determining the lifting force of the roll box are presented. To study the kinematics of lifting the roll box, a method and a test bench have been developed. According to him, when the roll box was raised, its movement was recorded on video, the image was processed using the After Effect and CorelDraw programs, and the movement of the rod attachment point to the roll box was determined. And also the equation for changing the angle of rotation of the roll box is determined using the Matlab Curve Fiting program.

The Causes of Hiking Ethiopian Consumer Prices

A growing consumer price is creating instability in the macroeconomic environment and hinders the consumption level of especially the poor society.This paper then explored the major causes of such increasing consumer prices using Ethiopian cases.Using data from the National Bank of Ethiopia from 1982/1983 to 2019/2020,it condensed the information of monetary sector,external sector and fiscal sector variables to a small set to estimate the causes of Ethiopian consumer price hiking using the ARDL model.The factors determining consumer price differ from food to non-food.The most important factors determining food price are price expectation and fiscal factors.On the other hand,the main determinant of non-food consumer prices is the fiscal factor.The author also found evidence of fiscal factors and price expectation effects on general consumer prices.Therefore,to contain the rise in consumer prices,it needs to exercise conservative fiscal stances,which require minimizing deficit financing,reducing the import tax rate and reducing domestic indirect tax rates such as excise tax and value added tax on basic consumer goods and services.Moreover,sound government policies are essential to address inflation anticipations(providing information for society about the future of inflation)to change public opinion.

Earth＇s Temporal Principal Moments of Inertia and Variable Rotation

Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth＇s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10^ 8 mas/yr; the third component of the rotational angular velocity, ω3 , has a decrease of 1.0×10^ 22 rad/s^2, which is around 23% of the present observed value. Studies show in detail that both 0 and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.

Moment tensor inversion of the November 6, 1988 MS=7.6, Lancang-Gengma, China,earthquake using long-period body-waves data

Moment tensor inversion was carried out to myert the source mechanism and source time function of the Ms=7.6November 6. 1988, Lancang-Gengma. Yunnan Province, Chin4 earthquake. Waveforms of long-period bodywaves recorded by China Digital Seismograph Network (CDSN) were used in the inversion. The inverted resultshows one nodal plane of right-lateral strike-slip faulting and another of left-lateral strike-slip faulting and a simplesource time function of a duration of about 15 s and scalar seismic moment of 6.4x 102oN-N-m From the geologicaldata and tectonic settings and also from field observations and epicentral distribution of aftershocks, the nodalplane striking in the azimuth of 313° is preferred as the fault plane. The pressure axis lies almost horizontally innorth-south direction.

Operation and Force Analysis of the Guide Wire in a Minimally Invasive Vascular Interventional Surgery Robot System

To develop a robot system for minimally invasive surgery is significant,however the existing minimally invasive surgery robots are not applicable in practical operations,due to their limited functioning and weaker perception.A novel wire feeder is proposed for minimally invasive vascular interventional surgery.It is used for assisting surgeons in delivering a guide wire,balloon and stenting into a specific lesion location.By contrasting those existing wire feeders,the motion methods for delivering and rotating the guide wire in blood vessel are described,and their mechanical realization is presented.A new resistant force detecting method is given in details.The change of the resistance force can help the operator feel the block or embolism existing in front of the guide wire.The driving torque for rotating the guide wire is developed at different positions.Using the CT reconstruction image and extracted vessel paths,the path equation of the blood vessel is obtained.Combining the shapes of the guide wire outside the blood vessel,the whole bending equation of the guide wire is obtained.That is a risk criterion in the delivering process.This process can make operations safer and man-machine interaction more reliable.A novel surgery robot for feeding guide wire is designed,and a risk criterion for the system is given.

ANALYSIS OF METHOD FOR DETERMINING AZIMUTH OF PRINCIPAL AXIS OF INERTIA BASED ON DYNAMIC BALANCE MEASUREMENT

The dynamic balance quality of a rotating object is an important factor to maintain the stability and accuracy for motion. The azimuth of the principal axis of inertia is a major sign of dynamic balance. A usual method is measuring moment of inertia matrix relative to some base coordinates on a rotary inertia machine so as to calculate the azimuth of principal axis of inertia, By using the measured unbalance results on the two trimmed planes on a vertical hard bearing double-plane dynamic balancing machine, the dimension and direction of couple unbalance can be found. An azimuth angle formula for the principal axis of inertia is derived and is solved by using unbalance quantities. The experiments indicate that method based on dynamic balancing measurement is proved rational and effective and has a fine precision.

The Vibration of Partially Filled Cylindrical Tank Subjected to Variable Acceleration

In this study, the vibration of a cylindrical tank partially filled with liquid under motion modeled as mass lumped is investigated. A three-dimensional quasi-static model of a partially-filled tank of circular cross-section is developed and integrated into a comprehensive three-dimensional vehicle model to study its dynamic performance as a function of acceleration, and the fill volume. The liquid load movement occurring in the roll and pitch planes of the tank is derived as a function of the longitudinal acceleration, and then the corresponding shifted load is expressed in terms of center of mass coordinates and mass moments of inertia of the liquid bulk, assuming negligible influence of fundamental slosh frequency and viscous effects. The vibration characteristics of the partially filled tank vehicle are evaluated in terms of load shift, forces and moments induced by the cargo movement, and dynamic load transfer in the longitudinal direction. The semi analytical response is obtained by means of SimuLink? Matlab Software. The effects of longitudinal acceleration of the tank system on the liquid surface inclination and consequently shifting of centroids and moment of inertia are illustrated.

A Measuring Method on Moment of Inertia of Large-scale Ammunition

A compound pendulum based measurement method is put forward and the relevant equipment is designed. By using the variation of angle with the time acquired by an angular displacement sensor, the moment of inertia is obtained through the numerical solution of certain equations, which are deduced from the phase-plane analysis of compound pendulum. The influences of both friction and air resistance on the compound pendulum are already taken into consideration without estimating and measuring the resistances in advance. With this method, the to-be-measured object can be positioned and fixed easily and safely. Numerical simulations show a favorable precision of this method.

Uncertainty analysis of ship model vertical center of gravity and transverse moment of inertia test

The usability of test results of ship model vertical center of gravity and transverse moment of inertia is generally depends on its uncertainty. Referring to the guidelines for uncertainty analysis in examination of liquid dynamic recommended by International Towing Tank Conference （ ITTC）, the results were analyzed, bias limits and precision limits were calculated and total uncertainty was estimated. The total uncertainty of six tests on ship model vertical center of gravity is is 0. 16% of the mean value, and the total uncertainty of six tests on ship model transverse moment of inertia is 5.66% of the mean value. The test results show that the total uncertainty of both the multiple tests and the single test is from the precision limits of ship model vertical center of gravity and transverse moment of inertia tests. Thus, the improved measurement system stability can enormously decrease the total uncertainty of multiple tests and the single test.

Research of the Issue of Lightening the Construction of the Gin Saw Cylinder

The article investigates the problem of lightening the construction of the saw cylinder of the gin by drilling a central longitudinal through hole on the shaft and cutting circular holes on the saw blades. This is accompanied by a relatively large decrease in the mass of the saw cylinder and a relatively smaller decrease in the axial moment of inertia of the cross-sectional area of the shaft, which provides the maximum deflection of the saw cylinder under the action of its own gravity in the middle of the span is from 0.450 mm to 0.406 mm.

Coupling Analysis of Moment of Inertia & Dynamic on Optoelectronic Tracking Turntable

With photoelectric tracking system as the research object,based on the theorem of moment of momentum and Euler dynamic equation,Nonlinear biaxial coupling dynamic model of tracking turntable is established.Effects of moment of inertia coupling,speed coupling and the dynamic coupling between tracking turntable shafts were studied,the analytical relation between them was given in theory.Verify the change trend of theoretical model.And it provides the theory reference and model base,for the future design of the high precision tracking controller And control parameter selection and optimization.In the end,specific measures are made for structure optimization.

Measurement of Moment of Inertia Based on Hilbert Transform

A measurement model based on torsion pendulum was established,in which nonlinear damping and nonlinear restoring force were considered.The calculation method of the moment of inertia was based on Hilbert transform.The motion of torsion pendulum showed the time-frequency characteristics due to the nonlinear factors,which were validated by the experimental data.The analytical signal was formed by Hilbert transform of the angular displacement signal of the test object.The moment of inertia can be computed by the instantaneous undamped natural frequency with Hilbert transform.Prior to the implementation of Hilbert transform,the empirical mode decomposition was used to filter the experimental signal.The moment of inertia of the test object was measured by the torsion pendulum system.The experimental results show that the relative measurement error of the moment of inertia was within 0.7%,which indicated the validity of the measurement method.

Description of the Superdeformed Bands of the Odd-Odd Nuclei in A ～ 150 Region

With the supersymmetry scheme including many-body interactions, the global property and the △I ＝ 4bifurcation in the superdeformed (SD) bands of odd-odd nuclei in A ～ 150 mass region are investigated systematically.Good results for the γ-ray energies, the dynamical moments of inertia, and energy differences △ Eγ - △ Erefγ are obtained.It shows that this approach is quite powerful in describing not only the SD bands in even-even and odd-A nuclei butalso those in odd-odd nuclei in the mass region.

The Physics of Rotational Flattening and the Point Core Model

The effect of rotation on the shape (figure) and gravitational quadrupole of astronomical bodies is calculated by using an approximate point core model: A point mass at the center of an ellipsoidal homogeneous fluid. Maclaurin’s analytical result for homogenous bodies generalizes to this model and leads to very accurate analytical results connecting the three observables: oblateness (ò), gravitational quadrupole (J2), and angular velocity parameter (q). The analytical results are compared to observational data for the planets and a good agreement is found. Oscillations near equilibrium are studied within the model.

Description of the Superdeformed Bands of Odd-Odd Nuclei in A～80 Region

Properties of the superdeformed bands of odd-odd nuclei in A ～ 80 massregion are investigated system-atically within the supersymmetry scheme including many-bodyinteractions and a perturbation possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry.The obtained γ-ray energies, and the dynamical moments of inertia agree with experimental data. Itshows that this approach is quite powerful in describing odd-odd nuclei in A ～ 80 mass region.