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.

Torque Free Axi-Symmetric Gyros with Changing Moments of Inertia

The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion. It shall be understood that the symmetry can be expressed by the notation (A=B) which does not presuppose geometric symmetry, where A and B are the principle moments of inertia about x and y axes respectively. We study the case of a torque free gyro upon which no external torque is acting. The equations of motion are derived when the origin of the xyz-coordinate system coincides with the gyro’s mass center c. This study is useful for the satellites, which have rotational symmetry and changed inertia moments, the antennas and the solar power collector systems.

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.

Nonadditivity in moments of inertia of high-K multiquasiparticle bands

The experimental high-K 2- and 3-quasiparticle bands of well deformed rare-earth nuclei are analyzed. It is found that there exists significant nonadditivity in moments of inertia （MOIs） for these bands. The microscopic mechanism of the rotational bands is investigated by the particle number conserving （PNC） method in the frame of cranked shell model with pairing, in which the blocking effects are taken care of exactly. The experimental rotational frequency dependence of these bands is well reproduced in PNC calculations. The nonadditivity in MOIs originates from the destructive interference between Pauli blocking effects.

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.

Systematic study of kinematic and dynamic moments of inertia of superdeformed bands with NpNn scheme

The systematics of kinematic moment of inertia J and dynamic moment of inertia J of superdeformed（SD） bands in A -130, 150, 190 mass regions have been studied. We have obtained the values of J^（1） and J^（2）for all the SD bands observed in the A-130, 150, 190 mass regions by using the experimental intraband E2 transition energies. The result of this work includes the variation of J with the product of valence proton and neutron numbers（NpNn）. The phenomenon of band mixing has been observed in the A -130, 150 mass regions and band crossing has been observed in the A-190 mass region. The systematics also includes the variation of J with the product of valence proton and neutron numbers（NpNn）. Evidence of staggering behaviour has been observed in all three A-130, 150 and 190 mass regions. We present for the first time the variation of J^（1）and J^（2）of SD bands in the A-130, 150, 190 mass regions with NpNn.

Improved Units of Measure in Rotational Mechanics

The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.

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.

Mechanical model study of relationship of molecular configuration and multiphase in liquid crystal materials

A mechanical model of liquid crystals （LCs） is applied to study the polymorphism of homologous series of terphenyl compounds. With a senti-experimental molecular orbit method, we calculate the moment of inertia which represents the rotation state to describe the phase transition temperature obtained from experimental data. We propose a novel explanation of the phase sequence or polymorphism of LC materials using the two key parameters, the moment of inertia and critical rotational velocity. The effect of molecular polarity on the appearance of liquid crystalline is also discussed.

Hydrodynamic Analysis of C-start in Crucian Carp

The kinematics of turning maneuvers of startled Crucian Carp (Carassius auratus) are presented. All escape responses observed are C-type fast-starts. The position of the center of mass and the moment of inertia of the fish are calculated. The results show that the position of the center of mass is always at 35% of the length of the fish from the head and the position of the center of mass and moment of inertia can be considered unchanged during C-start of Crucian Carp. Hydrodynamic analysis of the C-start is given based on the kinematics data from our experiments. The C-start consists of three stages. In stage 1, the tail fin of fish rapidly flaps in one direction, and a large moment acts on the fish′s body, which rotates around the center of mass with an angular acceleration. In stage 2, the tail fin flaps more slowly in the opposite direction at slower speed, the fish′s body rotates around the center of mass with angular deceleration and the center of mass of the fish moves along an arc. In stage 3, the moment approximately equals zero, the fish′s body stops rotating and the center of mass the moves along a straight line.

Properties of hyperon stars rotating at Keplerian frequency

The structure and properties of a Keplerian rotating hyperon star with an equation of state （EOS） investigated using the relativistic σ-ω-p model are examined by employing an accurate numerical scheme. It is shown that there is a clear rotating effect on the structure and properties, and that hyperon star matter cannot support a star with a mass larger than 1.9 M~, even a star rotating at the fastest allowed frequency. The constraints of the two known fastest rotating frequencies （716 Hz and 1122 Hz） on the mass and radius of a hyperon star are also explored. ~rthermore, our results indicate that the imprint of the rapid rotation of a hyperon star on the moment of inertia is clear; the backward equatorial redshift, the forward equatorial redshift and the polar redshift can be distinguished clearly, the forward equatorial redshift is always negative; and its figuration is far from a spherical symmetric shape.

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.

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.

Comparative Phenomenological Description of Even-Even Isotopes at Mass Region A ≈ 70

In the present work the nuclear structure properties and the backbending phenomena of even-even isotopes at A ≈ 70 mass region are analyzed using two simultaneous theoretical models based on a simple modified version of the collective model predictions besides an improved version of exponential model with the inclusion of pairing correlation. In general, both models successfully describe the backbending phenomena in that region. From the comparison between the predictions of the two proposed models a firm conclusion is obtained concerning the superiority of the simple improved version of the exponential model in describing the forward and down-bending region of the φ-ω2 plots.

Study of Even ^(230-238)U Isotopes by Using Cranked Nilsson Model,Single Particle Schrodinger Fluid and Collective Model

The Cranking Nilsson model is applied to calculate the single-particle energy eigenvalues and eigenfunctions of nuclei in a strongly deformed potential. Accordingly, The L. D. Energy, the Strutinsky inertia, the L. D. inertia, the volume conservation factor , the smoothed energy, the BCS energy, the G-value and the electric quadrupole moment of the five uranium isotopes: 230U, 232U, 234U, 236U and 238U are calculated as functions of the deformation parameter. Furthermore, the single-particle Schrodinger fluid is applied to calculate the rigid-body model, the cranking-model and the equilibrium-model moments of inertia of the five uranium isotopes. Moreover, the collective model is applied to calculate the rotational energies of these isotopes. The best potential and deformation parameters are also given.

Gravitational Potential of Asteroids of Diverse Shapes

Asteroid research is of global security interest, we are more afraid about any impact of these asteroids on Earth. We seek through this work to provide a study on the effect of the asteroid’s shape on the gravity aspect. Knowledge of the potential is crucial to bodies approaching the asteroid. There is a range of asteroid shapes to consider. Some well-known asteroids such Ceres, Vesta, Iris and Oumuamua are considered in this study. After determining the moment of inertia of the asteroids depending on their materials, the gravity fields and the potential gravity of the asteroids are established when varying their shapes. A representation of the gravity field is given in three dimensional coordinate systems. Also, the behavior of the potential gravity is drawing in the function of the object’s location. The second part is dealing with the interpretation of all the obtained results in order to deduce some rules and features which would be useful for the identification of the asteroids. Thus, by the best knowledge of the effect of the asteroid’s shape, we would be more informed in the survey of the hazardous near earth objects.

An improved HSFR method for natural vibration analysis of an immersed cylinder pile with a tip mass

Immersed cylinder piles are usually modelled as immersed carrying a tip mass and rotary moment of inertia. In this paper, an immersed cylinder pile along transversal modes of vibration are of water and structural damping are included in the formulation. cantilever cylinder columns the equations of motion of developed. Compressibility Natural frequencies of the immersed pile are obtained from the developed equations using harmonic sweep frequency response analyses. The proposed method is applied to numerical examples, and the results obtained are shown satisfactory when compared to other numerical solutions in the literature, or to finite element solutions and experimental data.

Virtual Inertia Estimation Method of DFIG-based Wind Farm with Additional Frequency Control

With the increasing penetration of wind power,using wind turbines to participate in the frequency regulation to support power system has become a clear consensus.To accurately quantify the inertia provided by the doubly-fed induction generator(DFIG)based wind farm,the frequency response model of DFIG with additional frequency control is established,and then by using Routh approximation,the explicit expression of the virtual moment of inertia is derived for the DFIG gridconnected system.To further enhance the availability of the expression,an estimation method is proposed based on the matrix pencil method and the least squares algorithm for estimating the virtual moment of inertia provided by the wind farm.Finally,numerical results tested by a DFIG grid-connected system and a modified IEEE 30-bus system verify the derived expression of the virtual moment of inertia and the proposed estimation method.

On the moment of inertia of a proto neutron star

The influences of σ^＊ and Ф mesons, temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star （PNS） are examined in the framework of relativistic mean field theory for the baryon octet {n, p, A, ∑^-, ∑^,∑^＋,^-, ^0} system. It is found that, compared with that without considering σ^＊ and Ф mesons, the moment of inertia decreases. It is also found that the higher the temperature, the larger the incompressibility and symmetry energy coefficient, and the larger the moment of inertia of a PNS. The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ^＊ and Ф mesons.