THE DRAG EXERTED BY AN OBLATE ROTATING ATMOSPHERE ON AN ARTIFICIAL SATELLITE

A theory is formulated for the motion of an artificial satellite under the joint effects of Earth oblateness and atmospheric drag. The Hamilton ' s equations of motion are derived including the zonal harmonics of the geopotential up to J4 and the drag accelerations. The atmospheric model is an oblate rotating model in which the atmospheric rotation lags behind that of the Earth as the increasing distance from the Earth. The drag free problem is first solved via two canonical transformations to eliminate in succession the short and long period terms. An operator D is then defined and used to formulate the drag acceleration in terms of the double primed variables expressing the solution of the drag-free problem.

Coexistence of Prolate and Oblate Shapes in ^(98)Sr Nuclei Using IBM2

The properties of the low-lying states and the shape coexistence in 98Sr are investigated within the framework of the proton-neutron interacting boson model （IBM2）. By considering the relative energy of the d proton boson to be different from that of the neutron boson, it is found that the calculated energy levels and the B（E2） transition strengths agree with the experimental data perfectly. Particularly, the second 0＋ state, which is associated with the shape coexistence phenomenon and has the lowest energy E（O＋） among all known even-even nuclei, is reproduced very well. The behavior of the calculated quadrupole shape invariants is consistent with the experimental results.

THE THREE-DIMENSIONAL FUNDAMENTAL SOLUTION TO STOKES FLOW IN THE OBLATE SPHEROIDAL COORDINATES WITH APPLICATIONS TO MULTIPLES SPHEROID PROBLEMS

A new three-dimensional fundamental solution to the Stokes flow was proposed by transforming the solid harmonic functions in Lamb's solution into expressions in terms Of the oblate spheroidal coordinates. These fundamental solutions are advantageous in treating flows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids. The least squares technique was adopted herein so that the convergence difficulties often encountered in solving three-dimensional problems were completely avoided. The examples demonstrate that present approach is highly accurate, consistently stable and computationally efficient. The oblate spheroid may be used to model a variety of particle shapes between a circular disk and a sphere. For the first time, the effect of various geometric factors on the forces and torques exerted on two oblate spheroids were systematically studied by using the proposed fundamental solutions. The generality of this approach was illustrated by two problems of three spheroids.

Dielectric Behavior of Oblate Spheroidal Particles：Application to Erythrocytes Suspensions

We have investigated the pressure effect on the eletrorotation (ER) spectrum of living cell suspensions byconsidering the particle shape effect. In particular, we consider coated oblate spheroidal particles and present a theoreticalstudy of ER based on the spectral representation theory. Analytic expressions for the characteristic frequency as wellas the dispersion strength can be obtained, thus simplifying the fitting of experimental data on oblate spheroidal cellsthat abound in the literature. From the theoretical analysis, we find that the cellshape, coating as well as materialparameters can change the ER spectrum. We demonstrate a good agreement between our theoretical predictions andexperimental data on human erthrocytes suspensions.

Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary

This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.

Correction on Effect of Earth’s Oblateness in Inversion of GPS Occultation Data

By using observed CHAMP orbit ephemeredes and MSISE90 dry air model and regarding the earth as a sphere and an ellipsoid respectively, phase delays are simulated and the simulated data are retrieved under different schemes. The comparison between the inverted temperature profiles and the model temperature profiles shows that by inverting observed data, we will get temperature results with large errors if the effect of Earth’s oblateness is omitted. The correction method is proved to be effective because the temperature errors decreased obviously with this method.

Existence of Equilibrium Points in the R3BP with Variable Mass When the Smaller Primary is an Oblate Spheroid

The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.

Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids

This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.

Lissajous Orbits at the Collinear Libration Points in the Restricted Three-Body Problem with Oblateness

In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbits around these points are investigated for the Earth-Moon system. The Lissajous orbits and the phase spaces are obtained under the effect of oblateness.

The Collinear Libration Points in the Elliptic R3BP with a Triaxial Primary and an Oblate Secondary

This paper examines the motion of a dust grain around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of collinear libration points. The positions and stability of these points are found to be affected by the triaxiality and oblateness of the primaries, and by the semi-major axis and eccentricity of their orbits. The stability behavior of the collinear points however remains unchanged;they are unstable in the Lyapunov sense.

Riemannian Acceleration in Oblate Spheroidal Coordinate System

The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate and realistic description of motion in these bodies can be realized. In this paper, we derive the Riemannian acceleration for motion in oblate spheroidal coordinate system using the golden metric tensor in oblate spheroidal coordinates. The Riemannian acceleration in the oblate spheroidal coordinate system reduces to the pure Newtonian acceleration in the limit of c0 and contains post-Newtonian correction terms of all orders of c-2. The result obtained thereby opens the way for further studies and applications of the motion of particles in oblate spheroidal coordinate system.

Oblateness Effect of Saturn on Halo Orbits of L1 and L2 in Saturn-Satellites Restricted Three-Body Problem

The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbits around L1 and L2 for the seven satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus) of Saturn in the frame work of CRTBP. It is found that the oblateness effect of Saturn on the halo orbits of the satellites closer to Saturn has significant effect compared to the satellites away from it. The halo orbits L1 and L2 are found to move towards Saturn with oblateness.

Analysis of Effect of Oblateness of Smaller Primary on the Evolution of Periodic Orbits

Evolution of periodic orbits in Sun-Mars and Sun-Earth systems are analyzed using Poincare surface of section technique and the effects of oblateness of smaller primary on these orbits are considered. It is observed that oblateness of smaller primary has substantial effect on period, orbit’s shape, size and their position in the phase space. Since these orbits can be used for the design of low energy transfer trajectories, so perturbations due to planetary oblateness has to be understood and should be taken care of during trajectory design. In this paper, detailed stability analysis of periodic orbit having three loops is given for A2 = 0.0001.

Evolution of the “f” Family Orbits in the Photo Gravitational Sun-Saturn System with Oblateness

We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.

Natural coupled orbit-attitude periodic motions in the perturbed-CRTBP including radiated primary and oblate secondary

This study investigated periodic coupled orbit-attitude motions within the perturbed circular restricted three-body problem(P-CRTBP)concerning the perturbations of a radiated massive primary and an oblate secondary.The radiated massive primary was the Sun,and each planet in the solar system could be considered an oblate secondary.Because the problem has no closed-form solution,numerical methods were employed.Nevertheless,the general response of the problem could be non-periodic or periodic,which is significantly depended on the initial conditions of the orbit-attitude states.Therefore,the simultaneous orbit and attitude initial states correction(SOAISC)algorithm was introduced to achieve precise initial conditions.On the other side,the conventional initial guess vector was essential as the input of the correction algorithm and increased the probability of reaching more precise initial conditions.Thus,a new practical approach was developed in the form of an orbital correction algorithm to obtain the initial conditions for the periodic orbit of the P-CRTBP.This new proposed algorithm may be distinguished from previously presented orbital correction algorithms by its ability to propagate the P-CRTBP family orbits around the Lagrangian points using only one of the periodic orbits of the unperturbed CRTBP(U-CRTBP).In addition,the Poincarémap and Floquet theory search methods were used to recognize the various initial guesses for attitude parameters.Each of these search methods was able to identify different initial guesses for attitude states.Moreover,as a new innovation,these search methods were applied as a powerful tool to select the appropriate inertia ratio for a satellite to deliver periodic responses from the coupled model.Adding the mentioned perturbations to the U-CRTBP could lead to the more accurate modeling of the examination environment and a better understanding of a spacecraft's natural motion.A comparison between the orbit-attitude natural motions in the unperturbed and perturbed models was also conducted to show this claim.

Competition between collective oblate rotation and non-collective prolate K isomerism in neutron-rich tungsten isotopes

Recent experiments open up the possibility to investigate oblate rotation-aligned states and prolate high-K isomers in neutron-rich tungsten isotopes.In the present work,we perform the projected-shell-model calculations for A ～ 190 tungsten nuclei.The 190 W results are compared with experimental data.The observed 8 + isomer is assigned as a two-quasiproton K π = 8 + configuration.Low-lying high-K four-quasiparticle states are predicted.Of particular interest is the prediction of the K π = 20 + state in 190,192 W,which may form a long-lived spin trap.In competition with the prolate high-K states,rotational alignment leads to near-yrast collective oblate rotation.

Observation of signature inversion in the πh_(9/2)(×)νi_(13/2) oblate band

High-spin states in 190Tl have been studied via the 160Gd(35Cl, 5nγ) reaction. The level scheme, consisting of the π h9 /2 νi13/2 oblate band and a cascade with character of single particle excitations, has been established. Spin values have been firmly assigned to the oblate band in 190Tl, resulting in low-spin signature inversion in the π h9 /2 νi13/2 oblate band for the first time. Based on the similarity of the level structure in doubly odd Tl nuclei, spin values for the oblate bands in 192―200Tl should be re-assigned, and a consistent low-spin signature inversion has occurred in these oblate deformed nuclei. The low-spin signature inversion phenomena can be interpreted qualitatively by using the 2-quasiparticle plus rotor model including p-n residual interactions.

Oblate Superdeformed High-K States in Superheavy Nuclei

Configuration-constrained calculations of potential-energy surfaces for ^292 122 show the occurrence of multiquasiparticle high-K isomeric state at oblate superdeformation. Such state could play a unique role in superheavy nuclei, with possible long life time from enhanced difficulty in fission due to additional barrier at oblate deformation, retardation in a decay due to unpaired nucleons, and hindrance in γ-ray transition due to K forbiddenness.

The equation of chronoamperometric current on an oblate hemispheroid microelectrode and its verification

With the aspect of equivalent diffusion layer an analytical chronoamperometric current equation on an oblate hemispheroid microelectrode for reversible electrochemical condition is derived. To verify this equation the chronoammograms have been obtained with benzoquinone in McIlvaine buffer solution (pH 7.0) at a mercury oblate hemispheroid microelectrode. The experimental results agree with the theoretical conclusions.

A Numerical Study of Jet Propulsion of an Oblate Jellyfish Using a Momentum Exchange-Based Immersed Boundary-Lattice Boltzmann Method

In present paper,the locomotion of an oblate jellyfish is numerically investigated by using a momentum exchange-based immersed boundary-Lattice Boltzmann method based on a dynamic model describing the oblate jellyfish.The present investigation is agreed fairly well with the previous experimental works.The Reynolds number and the mass density of the jellyfish are found to have significant effects on the locomotion of the oblate jellyfish.Increasing Reynolds number,the motion frequency of the jellyfish becomes slow due to the reduced work done for the pulsations,and decreases and increases before and after the mass density ratio of the jellyfish to the carried fluid is 0.1.The total work increases rapidly at small mass density ratios and slowly increases to a constant value at large mass density ratio.Moreover,as mass density ratio increases,the maximum forward velocity significantly reduces in the contraction stage,while the minimum forward velocity increases in the relaxation stage.