Principal Moments Of Inertia Research Articles

2101 補ひずみエネルギーに着目したフレーム要素の最適断面主軸方向決定法とトポロジー最適化への応用(OS21 設計と最適化I)

2101 補ひずみエネルギーに着目したフレーム要素の最適断面主軸方向決定法とトポロジー最適化への応用(OS21 設計と最適化I)

An Accurate Model of Mercury’s Spin-Orbit Motion

AbstractOur work deals with the physical and dynamical causes that induce librations of Mercury around an equilibrium state defined by the 3:2 spin-orbit resonance. In order to integrate the spin-orbit motion of Mercury, we have used our gravitational model of the solar system including the Moon’s spin-orbit motion. This model, called SONYR (acronym of Spin-Orbit N-bodY Relativistic model), was previously built by Bois, Journet and Vokrouhlicky in accordance with the requirements of the Lunar Laser Ranging observational accuracy.Using the model, we have identified the main perturbations acting on the spin-orbit motion of Mercury such as the planetary interactions or the dynamical figure of the planet. Moreover, the complete rotation of Mercury exhibits two proper frequencies, namely 15.847 and 1066 years, and in addition one spin-orbit secular resonance (298 898 years). A new determination of the mean obliquity of Mercury has been proposed. Besides, we have identified in the Hermean librations the impact of the uncertainty of the greatest principal moment of inertia (C/MR2) on the obliquity as well as on the libration in longitude (2.3 mas and 0.45 as respectively for an increase of 1% on the C/MR2 value). These accurate relations have to be taken into account in the context of the two upcoming missions BepiColombo and MESSENGER.

Origin of Spontaneous Electric Dipoles in Homonuclear Niobium Clusters

Surprisingly large, spontaneous electric dipole moments recently observed in homonuclear niobium clusters below 100 K are explained using first-principles electronic structure calculations. The calculated moments for Nb(n) (n < or =15) generally agree with the experimental data. A strong correlation is found between the geometrical asymmetry of the cluster and electric dipole: its magnitude is proportional to the spread in the principal moments of inertia and its direction aligns with the axis of the largest principal moment. Charge deformation densities reveal directional, partially covalent bonds that stabilize structural asymmetry. Classical simulations of the deflection of a cluster in a molecular beam reveal that the electronic dipole may persist at higher temperatures, but is masked by the rotational dynamics of the cluster.

Celestial mechanics of planet shells

The motion of a planet consisting of an external shell (mantle) and a core (rigid body), which are connected by a visco-elastic layer and mutually gravitationally interact with each other and with an external celestial body (considered as a material point), is studied (Barkin, 1999, 2002a,b; Vilke, 2004). Relative motions of the core and mantle are studied on the assumption that the centres of mass of the planet and external body move on unperturbed Keplerian orbits around the general centre of mass of the system. The core and mantle of the planet have axial symmetry and have different principal moments of inertia. The differential action of the external body on the core and mantle cause the periodic relative displacements of their centres of mass and their relative turns. An approximate solution of the problem was obtained on the basis of the linearization, averaging and small-parameter methods. The obtained analytical results are applied to the study of the possible relative displacements of the core an...

A characterisation of the complex vinyl fluoride⋯hydrogen fluoride by rotational spectroscopy and ab initio calculations

Combined use of rotational spectroscopy and ab initio calculations at the MP2/6-311++G(d,p) level of theory shows that the complex formed between vinyl fluoride and hydrogen fluoride has a planar geometry in which HF forms a hydrogen bond to the F atom of vinyl fluoride. With ϕ = the angle CF⋯H = 121.4° assumed from the ab initio calculation, the distance r(FH) = 1.892(14) Å and the angular deviation θ = 18.7(15)° of the F⋯H–F nuclei from collinearity were obtained by fitting the principal moments of inertia of the two isotopomers C 2H 3F⋯HF and C 2H 3F⋯DF investigated.

Stability of motion of a solid in the Steklov's case

We consider motion of a solid about a fixed point O in a uniform gravity field. The weight of the body is mg, and the distance from the center of gravity to the fixed point is l. Let Oxyz be a reference system rigidly connected to the body and its axes be the principal inertia axes of the body with respect to point O. The symbols A, B, and C denote the corresponding principal moments of inertia. The reference system OXYZ is fixed, and its OZ axis is directed upward. The notation p, q, r and γ1, γ2, γ3 corresponds to the components of the angular velocity for the body and of the unit vector of the ascending vertical axis OZ in the mobile reference system Oxyz. In the Steklov’s case [1], it is assumed that the center of gravity lies on the principal inertia axis. Let it be Ox axis. The Euler–Poisson equations have the form

What makes bowling balls hook?

This article presents exact equations of motion for a rotating bowling ball in a form that explicitly separates contributions due to nonequal principal moments of inertia, center-of-mass offset, and friction between the ball and lane. A computer program that solves the equations demonstrates that all of these factors are important for a realistic analysis of bowling. These factors significantly affect how much balls hook, that is, deflect sideways and approach the pins at an oblique angle. Simulations that approximate real bowling conditions indicate that the largest contribution comes from variable friction along the lane, that is, bowling lanes are generally prepared so that lane friction is higher by a factor of 2 or more along the last one-third of the ball’s trajectory. The analysis supports most (but not all) of the guidelines that bowlers have developed for predicting ball performance.

Quantifying deficits in the 3D force capabilities of a digit caused by selective paralysis: application to the thumb with simulated low ulnar nerve palsy

We present the development of a vision-feedback method to characterize how selective paralysis distorts the three-dimensional (3D) volume representing digit-tip force production capability and its application to healthy individuals producing thumb-tip force with and without simulated low ulnar nerve palsy (LUNP). Subjects produced maximal static voluntary force spanning the transverse, sagittal and frontal planes of the thumb (16, 15 and 10 subjects, respectively). Subjects produced thumb-tip force tasks in guided and self-selected directions. The envelope (convex hull) of extreme forces in each plane approximated that cross-section of the 3D volume of force capability. Some subjects repeated the tasks with a temporary ulnar nerve block applied at the wrist to simulate complete acute LUNP. Three geometric properties of the force convex hull characterized each cross-section's shape: the ratios of its principal moments of inertia (RPMIs), the orientation of its principal axis (OPA), and its centroid location. Our results show that force production in the thumb's sagittal plane may be a reproducible and objective test to grade motor impairment in LUNP: paired t-tests of the larger RPMI in this plane best distinguished the nerve-blocked cases from the control cases in the guided task ( p=0.012), and Discriminant Analysis of the centroid location for the self-selected task in this plane correctly classified 94.7% of subjects into the control and ulnar nerve-blocked groups. We show that our method measures and detects changes in a digit's force production capabilities. Towards a clinical test of motor impairment in LUNP, this biomechanical study dictates which 3D thumb-tip forces to measure (those in the sagittal plane) and how to measure them (using the self-selected task).

Motion of a Planet with a Complex Structure

The motion of a planet consisting of a mantle and a core (solid bodies) connected by a viscoelastic layer and interacting with each other and an external point mass by the law of gravitation is considered. The mutual motions of the core and mantle are investigated assuming that the centers of mass of the planet and external point mass moves along undisturbed Keplerian orbits around the common center of mass of the system. The planetary core and mantle have an axial symmetry and different principal moments of inertia, which leads to a displacement of the center of mantle relative to the center of core and to their mutual rotations. The results obtained on the basis of averaged equations are illustrated by the example of the Earth–Moon system.

Asteroid 1620 Geographos: III. Inelastic Relaxation in the Vicinity of the Poles

The rate of inelastic relaxation of asteroid 1620 Geographos in the vicinity of the poles, corresponding to rotation about the axes of minimal and maximal principal moment of inertia, was considered on the basis of the theory stated by Efroimsky and Lazaryan. The low bound of the total relaxation time is estimated as 4 × 106 years.

Theory of the Mercury's spin-orbit motion and analysis of its main librations

The upcoming space missions, MESSENGER and BepiColombo with onboard instrumentation capable of measuring the rotational parameters stimulate the objective to reach an accurate theory of the rotational motion of Mercury. For obtaining the real motion of Mercury, we have used our relativistic BJV model of solar system integration including the coupled spin-orbit motion of the Moon. We have extended this model by generalizing the spin-orbit couplings to the terrestrial planets, notably Mercury. The updated model is called SONYR (acronym of Spin-Orbit N-BodY Relativistic model). The SONYR model giving an accurate solution of the spin-orbit motion of Mercury permits to analyze the different families of the Hermean rotational librations. The spin-orbit motion of Mercury is characterized by two proper frequencies (namely 15.847 and 1066 years) and its 3:2 resonance presents a second synchronism which can be understood as a spin-orbit secular resonance (278 898 years). By using the SONYR model, we find a new determination of the mean obliquity, namely 1.6 arcminutes. Besides, we identify in the Hermean librations the impact of the uncertainty of the greatest principal moment of inertia (\cmr2) on the obliquity and on the libration in longitude (2.3 mas and 0.45 as respectively for an increase of 1% on the \cmr2 value). These determinations prove to be suitable for providing constraints on the internal structure of Mercury.

Non-Integrability of the Problem of a Rigid Satellite in Gravitational and Magnetic Fields

In this paper we analyse the integrability of a dynamical system describing the rotational motion of a rigid satellite under the influence of gravitational and magnetic fields. In our investigations we apply an extension of the Ziglin theory developed by Morales-Ruiz and Ramis. We prove that for a symmetric satellite the system does not admit an additional real meromorphic first integral except for one case when the value of the induced magnetic moment along the symmetry axis is related to the principal moments of inertia in a special way.

Haptically Perceiving Whole and Partial Rod Lengthat the Small Scale

Exteroception by dynamic touch has been studied for the most part using large (30-120 cm, 20-65 g) handheld stimulus objects. Only one study, Santana and Carello (1999), has looked at the perception of small-scale objects (15-25 cm, 0.75-1.3 g) by dynamic touch. The purpose of this article is to extend the theory of dynamic touch to the perception of small-scale objects. We explore whether the power-law scaling of perceived magnitudes to object inertial properties observed at the large scale held at the small scale, and whether partial and whole-length perceptions of small-scale objects were perceptually independent. Results indicated accurate whole-length perceptions but a change in the scaling of perceived whole length to the principal moment of inertia. Results also indicated inaccurate perceptions of partial length that were uncorrelated with object inertial properties. Perceptual independence of whole- and partial-length perceptions was observed.

Thermodynamic properties of chlorinated phenols, cyclo-C 5 compounds, and derived radicals from G3MP2B3 calculations

For a set of 17 selected chlorinated and polychlorinated phenols and cyclo-C 5 compounds, energy minimum structures, harmonic vibrational wavenumbers ω e, principal moments of inertia I A, I B, and I C, heat capacities C p o ( T), entropies S o ( T), thermal energy contents H o ( T)− H o (0), and standard enthalpies of formation Δ f H o ( T) were calculated at the ab initio G3MP2B3 level of theory and presented for T=298.15 K. The eight radicals of this set are characterized, in addition, by total atomic spin densities ρ as well as by isotropic hyperfine coupling constants A iso. The relationships between the radicals and their parent molecules are investigated, and the corresponding bond dissociation energies are presented.

Molecular shape diversity of combinatorial libraries: a prerequisite for broad bioactivity.

A computational method to rapidly assess and visualize the diversity in molecular shape associated with a given compound set has been developed. Normalized ratios of principal moments of inertia are plotted into two-dimensional triangular graphs and then used to compare the shape space covered by different compound sets, such as combinatorial libraries of varying size and composition. We have further developed a computational method to analyze interset similarity in terms of shape space coverage, which allows the shape redundancy between the different subsets of a given compound collection to be analyzed in a quantitative way. The shape space coverage has been found to originate mainly from the nature and the 3D-geometry (but not the size) of the central scaffold, while the number and nature of the peripheral substituents and conformational aspects were shown to be of minor importance. Substantial shape space coverage has been correlated with broad biological activity by applying the same shape analysis to collections of known bioactive compounds, such as MDDR and the GOLD-set. The aggregate of our results corroborates the intuitive notion that molecular shape is intimately linked to biological activity and that a high degree of shape (hence scaffold) diversity in screening collections will increase the odds of addressing a broad range of biological targets.

Estimation of the Earth's tensor of inertia from recent global gravity field solutions

The dynamic figure of the Earth, characterized by the principal axes and principal moments of inertia, is estimated from satellite-derived gravitational harmonic coefficients of second degree in recent global Earth gravity models and from the dynamic ellipticity resulting from the precession constant observed through very-long-baseline interferometry (VLBI). Closed, exact formulae for the determination of these parameters of the Earth's tensor of inertia are developed based on the exact solution of the eigenvalue–eigenvector problem, including a rigorous error propagation. These formulae are applied to determine (a) static components and accuracy of the Earth's tensor of inertia at epoch and (b) the variation with time of the Earth's tensor of inertia and its accuracy. The best-fitting principal moments of inertia and second-degree harmonic coefficients in the principal-axes system are found from an adjustment involving four global gravity field models and six different values for the dynamic ellipticity. The evolution with time of the dynamic figure of the Earth is determined from the mean pole path and the observed secular rate of change in the second-degree zonal coefficient. It is found that differences in the principal moments of inertia change significantly over the time interval from 1962 to 2000, whereas changes in the absolute values cannot be reliably resolved due to the uncertainty in the dynamic ellipticity.

Analytical Development of Rigid Mercury Nutation Series

In this paper, series of a rigid model of Mercury nutations are computed. The method used is based on the calculation of the forces produced by the Sun on Mercury as considered as a rigid body. In order to take into account the indirect effects coming from the orbit perturbations of Mercury, we used the ephemerides VSOP87 (Bretagnon and Francou, 1988). Due to non-negligible difference between the principal moment of inertia A and B in the case of Mercury, we compute also terms due to the triaxiality in addition to the general terms coming from J2. With a truncation level of 10−3 mas (milliarcsecond), related to the present-day precision of the Mercury precession constant, 173 terms in longitude (Δψ sin e) and 166 terms in obliquity (Δe) are computed. The value of the dynamical flattening used is HD = (C − A)/C = 2.3 × 10−4 (Anderson, 1987).

Collisional Relaxation of Luminescence Anisotropy in Rarefied Gases in the Condensed Phase

The orientational relaxation of optically induced anisotropy in rarefied gases and at a damped rotation has been investigated. It has been found that the anisotropy relaxation in rarefied gases is described by a reduced kinetic equation depending only on free rotation integrals. The behavior of the integral anisotropy of luminescence for free symmetric and asymmetric top molecules has been elucidated. The law of luminescence depolarization has been obtained for asymmetric top molecules in the Gordon J-diffusion model. It represents the sum of two Stern–Volmer-type dependences, whose relative contribution is determined by the orientation of the dipole moments of transitions with absorption and emission of light in the molecular coordinate system and by the principal moments of inertia of the molecular top. It has been established that in the limit of a strongly damped rotation, kinetic equations of the general form reduce to equations of rotational diffusion. A number of modified diffusion equations correctly describing the contribution of inertial effects to the orientational relaxation of anisotropy have been obtained.

Equilibrium structures for the cis and trans isomers of 1,2‐difluoroethylene and the cis,trans isomer of 1,4‐difluorobutadiene

AbstractMicrowave spectra for seven isotopomers of cis‐1,2‐difluoroethylene have been reinvestigated and extended with the pulsed‐molecular‐beam Fourier transform method. Rotational Hamiltonians that include a full set of quartic centrifugal distortion constants have been fit for each isotopomer. Ground‐state rotational constants for the trans isomer were available from an investigation of the high‐resolution infrared spectra of several isotopomers. Equilibrium rotational constants have been extracted for the cis and trans isomers from the experimental ground‐state constants and the vibration–rotation constants computed at the MP2/6‐31G(d) level. Equilibrium structures have been fit to the equilibrium principal moments of inertia for both isomers, and isomeric differences in the bond lengths and bond angles have been interpreted in terms of the strong influence of fluorine substitution. For cis,trans‐1,4‐difluorobutadiene a similar derivation of the equilibrium structure has been achieved through the combination of published microwave data and quantum chemical calculations. This substance provides an opportunity to examine the influence of cis and trans fluorine substitution within a single molecule. Evidence is weighed for the adequacy of vibration–rotation constants computed with the MP2/6‐31G(d) model. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Microwave Spectra of o-Fluorotoluene and Its 13C Isotopic Species: Methyl Internal Rotation and Molecular Structure

The rotational spectra of o-fluorotoluene and its seven 13C isotopic species were recorded in the frequency range from 4 to 20 GHz with employment of pulsed molecular beam Fourier-transform microwave (MB-FTMW) spectrometers. The analysis of the spectra in the two lowest states of methyl internal rotation (torsional ground state, A and E species) was based on a asymmetric frame-rigid symmetric top Hamiltonian with inclusion of centrifugal distortion terms, yielding structural rotational constants, as well as the threefold barrier V3 to internal rotation and the angle∢(a,i) between the principal moment of inertia a axis and the internal rotor axis i. The rotational constants of all eight isotopomeres were used to derive the seven 13C r s coordinates of the molecule.