Principal Moments Of Inertia Research Articles

New cases of regular precession of an asymmetric liquid-filled rigid body

To describe the rotation of a rigid body with an ellipsoidal cavity filled with an ideal vorticated liquid, the Poincare–Hough–Zhukovsky equations are used. It is obtained constraints (hereinafter referred to as configuration conditions) on the mass distribution and cavity dimensions of an asymmetric liquid-filled rigid body under which the rigid body can perform the regular precession. Two possible nontrivial cases are indicated when one or two components of the direct vector of the axis of proper rotation are equal to zero. It is shown that if the axis of proper rotation coincides with one of the principal axes of inertia of the system, it suffices to fulfill one configuration condition. The ratio between the periods of proper rotation and precession is found. The regular precession of a system in which the principal moments of inertia are close to each other and the cavity is close to spherical is considered. For the case when the difference between the two equatorial moments of inertia is an order of magnitude smaller than the difference between the equatorial and polar moments, the main part of the ratio between the periods coincides with the Euler period, and the correction is due to the inequality between the equatorial moments of inertia. In the case when the axis of proper rotation is orthogonal to a principal axis and is not coincident with any other principal axis, the number of configuration conditions is two. Expressions for the rates of precession and proper rotation are obtained, and the position in the body of the axis of proper rotation is indicated. Special cases are given that allow simplification of the configuration conditions.

Computational investigation on the reaction of dimethyl ether with nitric dioxide. I. Underlying mechanism and accurate energetics

The reaction of dimethyl ether (DME) with nitrogen dioxide (NO2), which plays a critical role in the low-temperature oxidation behavior of DME, is employed as prototype for reactions of heavier clean ether fuels to assess different hybrid density functionals and “double-hybrid” density functionals. The reaction energies and barrier heights for the reaction system were computed with CCSD(T) theory extrapolated to the complete basis set limit using augmented cc-pVDZ and cc-pVTZ basis sets. The involved energetics were also improved by the CCSD(T)/6-311+G(2df,2p), QCISD(T)/6-311+G(2df,2p), G3B3, G3MP2B3, CBS-QB3, G4, and G4MP2 calculations. It is shown that “double-hybrid” density functionals with the TZVP basis set can give accurate geometries and principal moments of inertia of reactants and products and the B2PLYP/TZVP level can achieve results for barrier heights comparable in accuracy to the high-level ab initio results, which is identified as an important potential theoretical level for direct kinetics studies on the rates of these and homologous reaction systems. The calculated results indicate that NO2 preferentially captures an out-of-plane hydrogen atom from the DME molecule by the O or the N end via three distinct channels to produce trans-HONO, cis-HONO, and HNO2, respectively, and each channel involves the formation of a van der Waals post-reaction adducts lying lower in energy than their separate products.

The study of the motion of a gyroscope without rotational symmetry

In rigid dynamics theory the gyroscope has a special role, as one of the bodies with the most complex motion, having three degrees of freedom. As consequence of the complexity of the motion is the fact that only for three situations, the equations of motion can be analytically integrated. For all the three situations, it is assumed that the principal moments of inertia (PMI) with respect to the principal axes that are normal to the rotation axes, are equal, condition fulfilled by the shape of body of revolution of the gyroscope. The paper analyses the case when the two principal moments of inertia are unequal. The equations of motion are numerically integrated for different values of the ratio between the two PMI. The effect of the disparity between the two PMI upon the motion of the gyroscope is proved by comparison with the motion of the axisymmetric gyroscope, both obtained by numerical integration.

Evolution of the obliquity of an exoplanet: A non-resonant case

We investigate analytically and numerically the variation of the obliquity (the axial tilt) of a hypothetical exo-Earth. A large number of exoplanets was discovered recently; since not much information is available about the masses and orbits of the stars and planets comprising a planetary exo-system, unlike for the planets of the Solar system, the problem is considered in a general setup. The exo-Earth is assumed to be rigid, axially symmetric and almost spherical, the difference between the largest and the smallest principal moments of inertia being a small parameter of the problem. Assuming the orbits of the celestial bodies to be quasiperiodic, we apply time averaging to study rotation of the exo-Earth at times large compared to the respective periods. In the present paper, we consider the case of non-resonant frequencies; we intend to study resonances in the future. In addition, we investigate numerically how the range of obliquity of the exo-Earth in a particular system comprised of a star and two planets varies on modifying the geometry of the orbits, the mass of the second planet and the initial obliquity.

Fractal fluctuations in exploratory movements predict differences in dynamic touch capabilities between children with Attention-Deficit Hyperactivity Disorder and typical development.

Children with Attention-Deficit Hyperactivity Disorder (ADHD) struggle to perform a host of daily activities. Many of these involve forceful interaction with objects and thus implicate dynamic touch. Therefore, deficits in dynamic touch could underlie functional difficulties presented by ADHD children. We investigated whether performance on a dynamic touch task (length perception by wielding) differ between children with ADHD and age-matched controls. We further examined whether this difference could be explained by fractal temporal correlations (wielding dynamics). Forty-two children (ADHD: 21; typically developing: 21) wielded unseen wooden rods and reported their perceived length in the form of magnitude productions. The rods varied in the magnitude of the first principal moment of inertia (I1). Three-dimensional displacements of hand and rod positions were submitted to Detrended Fluctuation Analysis to estimate trial-by-trial temporal correlations. Children with ADHD reported shorter length for rods with higher I1 than their typically developing peers, indicative of reduced sensitivity to mechanical information supporting dynamic touch. Importantly, temporal correlations in wielding dynamics moderated children’s usage of I1. This finding points to a role of exploratory movements in perceptual deficits presented by children with ADHD and, thus, should be considered a new potential target for interventions.

Evidence for ligandable sites in structured RNA throughout the Protein Data Bank.

RNA has attracted considerable attention as a target for small molecules. However, methods to identify, study, and characterize suitable RNA targets have lagged behind strategies for protein targets. One approach that has received considerable attention for protein targets has been to utilize computational analysis to investigate ligandable "pockets" on proteins that are amenable to small molecule binding. These studies have shown that selected physical properties of pockets are important parameters that govern the ability of a structure to bind to small molecules. This work describes a similar analysis to study pockets on all RNAs in the Protein Data Bank (PDB). Using parameters such as buriedness, hydrophobicity, volume, and other properties, the set of all RNAs is analyzed and compared to all proteins. Considerable overlap is observed between the properties of pockets on RNAs and proteins. Thus, many RNAs are capable of populating conformations with pockets that are likely suitable for small molecule binding. Further, principal moment of inertia (PMI) calculations reveal that liganded RNAs exist in diverse structural space, much of which overlaps with protein structural space. Taken together, these results suggest that complex folded RNAs adopt unique structures with pockets that may represent viable opportunities for small molecule targeting.

On the Constructive Algorithm for Stability Analysis of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in the Case of Combinational Resonance

We deal with a Hamiltonian system with two degrees of freedom, whose Hamiltonian is a 2π-periodic function of time and analytic in a neighborhood of an equilibrium point. It is assumed that the characteristic equation of the system linearized in a neighborhood of the equilibrium point has two different double roots such that their absolute values are equal to unity, i. e., a combinational resonance takes place in this system. We consider the case of general position when the monodromy matrix of the linearized system is not diagonalizable. In this case the equilibrium point is linearly unstable. However, this does not imply its instability in the original nonlinear system. Rigorous conclusions on the stability can be formulated in terms of coefficients of the Hamiltonian normal form. We describe a constructive algorithm for constructing and normalizing the symplectic map generated by the phase flow of the Hamiltonian system considered. We obtain explicit relations between the coefficients of the generating function of the symplectic map and the coefficients of the Hamiltonian normal form. It allows us to formulate conditions of stability and instability in terms of coefficients of the above generating function. The developed algorithm is applied to solve the stability problem for oscillations of a satellite with plate mass geometry, that is, Jz = Jx + Jy, where Jx, Jy, Jz are the principal moments of inertia of the satellite, when the parameter values belong to a boundary of linear stability.

Numerical solutions of rotational normal modes of a triaxial two-layered anelastic Earth

The Earth's rotational normal modes depend on Earth model used, including the layer structures, principal inertia moments of different layers and the compliances. This study focuses on providing numerical solution of the rotational normal modes of a triaxial two-layered anelastic Earth model without external forces but with considering the complex forms of compliances and the electromagnetic coupling between the core and mantle. Based on the present knowledge of the Chandler wobble (CW) and Free Core Nutation (FCN), we provide a set of complete compliances which could be used for reference in further investigations. There are eight rotational normal mode solutions, four of which might exist in nature. However, in reality only two of these four solutions correspond to the present motion status of the prograde CW and the retrograde FCN. On one hand, our numerical calculations show that the periods and quality factors (Qs) of CW and FCN are respectively 434.90 and 429.86 mean solar days (d) and 76.56 and 23988.47 under frequency-dependent assumption, and the triaxiality prolongs CW about 0.01 d and has hardly effect on FCN. On the other hand, we analyze the sensibility of compliances and electromagnetic coupling parameter on the periods and Qs of CW and FCN and find the sensitive parameters with respect to them.

On Parameters of the Earth-Like Model of Venus

A brief review on the history of constructing Earth-like models of the Venusian interior is presented. Available observational data are analyzed. An explanation for the anomalously large ratio of the quadrupole gravitational moment J2 to the small parameter of Venus q is proposed. Thus, estimates were obtained for the precession constant and principal moments of inertia for the Earth-like model of Venus.

Pitting corrosion of reinforcing steel bars in chloride contaminated concrete

This paper experimentally investigates the pit corrosion of steel bars in chloride contaminated concrete. The obtained 3-D images of the corroded bars are analyzed using statistical methods. The results show that the pit depth, residual cross-section area and smaller principal moment of inertia of plane area have multiple probability distribution patterns. The correlation of the pit depth with the mass loss is weak. The statistically obtained locations where the minimum residual cross-section area and minimum smaller principal moment of inertia of plane area are located are found to be close, suggesting this is the weakest section where the corroded bar will likely fail.

Signature of Phobos’ interior structure in its gravity field and libration

The interior of the Martian moon Phobos has not been precisely determined yet, in spite of space missions sent at close distance to the body. The current measurements (imagery, astrometric, etc.) lead to controversial conclusions about the level of heterogeneity inside Phobos. Yet, the inside mass distribution is a signature of the conditions prevailing at its formation as well as of its evolution. Here, we study possible heterogenous mass distributions based on internal models built from surface observables and available bulk density and shape measurements. We identify four different families of mass distribution involving rocky material, (macro-)porosity and ice. Mass heterogeneities correspond to either an excess of porosity or a compaction of material under Stickney crater, or a deficit of porosity in the upper layers of Phobos, or a concentration of ice either in depth inside Phobos or in shallow layers. We then discretize the shape of Phobos using 500m-length cubes to fit its volume and total mass. We compute the possible distribution of these cubes for each family of internal mass heterogeneity model. We deduce the possible values of the principal moments of inertia as well as of the geodetic observables such as the libration amplitude and the gravity field anomalies (up to degree and order 10) associated with these models. A comparison of these computed observables between the different heterogeneity models and with their expected homogenous mass distribution values allow us to quantify the possible heterogeneity degree within Phobos. The computed heterogeneity observables can depart by tens of percent from the homogenous values. The most striking departures are from the interior model with mass excess (less porosity) or deficit (more porosity) beneath Stickney crater. In turn, measurements of libration amplitude and low degree coefficients of the gravity field at a precision better than 5% can allow to identify such kinds of heterogeneities mainly located beneath Stickney. Mass excess or deficit can therefore be also distinguished, which is of importance to identify whether Phobos was already porous or monolithic before the formation of Stickney. The current measurements of libration amplitude and degree-two gravity coefficient are quite uncertain, but seem to reject models with higher porosity under Stickney, favoring a pre-impact porous body. The icy models depart less from the homogenous signatures, hence requiring more precise measurements of the geodetic observables and of the shape of Phobos. The improvement of these measurements by the Mars Moon Explorer mission for instance could thus allow for better constraining our model of Phobos’ interior and bring further constraints for its formation.

The influence of anisotropic voxel caused by field of view setting on the accuracy of three-dimensional reconstruction of bone geometric models

The finite element method is playing an increasingly important role in osteoporosis screening. An accurate bone geometric model, a prerequisite for the finite element analysis, is affected by voxels. Isotropic voxel has advantages in three-dimensional reconstruction, but field of view setting usually results in anisotropic voxels. The main goal of this study was to investigate the influence of anisotropic voxel on the accuracy of three-dimensional reconstruction of bone geometric models. Sixty metatarsal bones were scanned twice with an interval of 18 months with different fields of view. We reconstructed these metatarsals and compared them. The results showed that there was no significant difference in volume, surface, length, width and height and two principal moments of inertia, indicating that anisotropic voxel caused by field of view setting has a neglectable effect on the three-dimensional reconstruction of bone geometric models, and that using finite element method based on bone geometric model reconstructed by anisotropic voxel to predict bone strength is reliable.

A generalized theory of the figure of the Earth: on the global dynamical flattening

A generalized theory of the figures of the Earth’s interior to a third-order precision of ellipticity is proposed in accompanying paper in which all the odd degree and nonzero order spherical harmonic terms are included. As both the direct and indirect contributions of the asymmetric crust are included, this theory makes a significant improvement for calculating the asymmetric equilibrium figures of the real Earth comparing with the traditional theories which can only deal with the ideal symmetric Earth. The principal moments of inertia (PMOI: A, B, C) and global dynamical flattening (H) are important quantities in studying the rotating Earth. Precession and gravity observations give observation value of H ( $$H_{\mathrm{obs}} \approx 1/305.4559$$ ) with very high precision, while its theoretical calculated value ( $$H_{\mathrm{theory}} \approx 1/308.5$$ ) from traditional theories and a starting symmetric Earth model (like PREM model) is about $$1\%$$ less than $$H_{\mathrm{obs}}$$ . Using the new theory in accompanying paper and replacing the homogeneous outermost crust and oceanic layers in PREM with CRUST1.0 model, we recalculate the equilibrium figures of the Earth’s interior and finally get new values of PMOI and $$H_{\mathrm{theory}}$$ ( $${\approx } \,1/304.7167$$ ) whose consistency with $$H_{\mathrm{obs}}$$ are significantly improved to 0.24%. Furthermore, the asymmetric figures of some interesting boundaries, like inner core boundary, core-mantle boundary, are also given as by-products of this work as these boundaries’ figures are key input for studies of their topographic effect on global rotation and geodynamics, like nutation, normal modes, especially like free core nutation.

Soybean oil-based nanoemulsion systems in absence and presence of curcumin: Molecular dynamics simulation approach

Curcumin is the most bioactive compound of turmeric (Curcuma longa) plant, which has a wide range of beneficial biological and pharmacological activities, including antioxidants, anti-inflammatory, and anti-cancer agents. The application of curcumin is limited due to low solubility and low bioavailability. Today, the use of nanotechnology in curcumin formulations has been considered to improve the performance of curcumin. Particularly nanoemulsions can be used as agents of increasing penetration in the pharmaceutical and food industries. Despite the extensive empirical research on nano-curcumin, the behavior and formation of the curcumin nanoemulsion have not been theoretically investigated. Molecular dynamics Simulation of nanoemulsion systems is performed to have a better understanding of molecular behavior. Here, the simulation was performed on the base on the ratios obtained in experimental work, and by reviewing the trajectory, the variety of assemblies was determined at different times. This study revealed that molecular assemblies formed in the absence and presence of curcumin have different size and arrangement. The Variety of assemblies was studied after reaching to the constant number of assemblies in the equilibrium. The average radius of gyrations was estimated for assemblies composed of more than three molecules in the curcumin nanoemulsion system and the effective radius of the different assemblies was determined based on the related relationship. The size of particles was determined to be in the range of 2–6.3 nm. The size of particles were determined to be in the range of 2–6.3 nm. The necessary information was gained by analyzing the average ratio of the principal moments of inertia in order to determine the shape of the assemblies and it was found that the assemblies have almost spherical and prolate spheroid shapes. Particle size and shape results were in good agreement with experimental results. The arrangement of various assemblies showed that all molecules except curcumin were placed into the assemblies in the way that hydrophobic and hydrophilic parts were located inside and at the surface of the assemblies, respectively. While curcumin selected surface in all assemblies.

PKIDB: A Curated, Annotated and Updated Database of Protein Kinase Inhibitors in Clinical Trials.

The number of protein kinase inhibitors (PKIs) approved worldwide continues to grow steadily, with 39 drugs approved in the period between 2001 and January 2018. PKIs on the market have been the subject of many reviews, and structure-property relationships specific to this class of drugs have been inferred. However, the large number of PKIs under development is often overlooked. In this paper, we present PKIDB (Protein Kinase Inhibitor Database), a monthly-updated database gathering approved PKIs as well as PKIs currently in clinical trials. The database compiles currently 180 inhibitors ranging from phase 0 to 4 clinical trials along with annotations extracted from seven public resources. The distribution and property ranges of standard physicochemical properties are presented. They can be used as filters to better prioritize compound selection for future screening campaigns. Interestingly, more than one-third of the kinase inhibitors violate at least one Lipinski’s rule. A Principal Component Analysis (PCA) reveals that Type-II inhibitors are mapped to a distinct chemical space as compared to orally administrated drugs as well as to other types of kinase inhibitors. Using a Principal Moment of Inertia (PMI) analysis, we show that PKIs under development tend to explore new shape territories as compared to approved PKIs. In order to facilitate the analysis of the protein space, the kinome tree has been annotated with all protein kinases being targeted by PKIs. Finally, we analyzed the pipeline of the pharmaceutical companies having PKIs on the market or still under development. We hope that this work will assist researchers in the kinase field in identifying and designing the next generation of kinase inhibitors for still untargeted kinases. The PKIDB database is freely accessible from a website at http://www.icoa.fr/pkidb and can be easily browsed through a user-friendly spreadsheet-like interface.

J plots: a new method for characterizing structures in the interstellar medium

Large scale surveys have brought about a revolution in astronomy. To analyse the resulting wealth of data, we need automated tools to identify, classify, and quantify the important underlying structures. We present here a method for classifying and quantifying a pixelated structure, based on its principal moments of inertia. The method enables us to automatically detect, and objectively compare, centrally condensed cores, elongated filaments and hollow rings. We illustrate the method by applying it to (i) observations of surface-density from Hi-GAL, and (ii) simulations of filament growth in a turbulent medium. We limit the discussion here to 2D data; in a future paper we will extend the method to 3D data.

Prospects of using a permanent magnetic end effector to despin and detumble an uncooperative target

Space debris, such as defunct satellites and upper stages of rockets, becomes an uncooperative target after losing its attitude control and communication ability. In addition, tumbling motion can occur due to environmental perturbations and residual angular momentum prior to the object’s end-of-mission. To minimize the collision risk during docking and capturing of the tumbling target, a non-contact method based on the eddy current effect is put forward to transmit the control torque to the tumbling target. The main idea is to induce a controllable torque on the conducting surface of the tumbling target using a rotational magnetic field generated by a Halbach rotor. The radial and axial Halbach rotors are used to damp the spinning and nutation motions of the target, respectively. The normal and tangential force are evaluated concerning the relative pose between the chaser and the target. A simplified dynamic model of the nutation damping and despinning processes is developed and the influences of the asymmetrical principal moments of inertia and transverse angular velocity are discussed. The numerical simulation results show that the designed Halbach rotor stabilized the target attitude within an acceptable time. The electromagnetic nutation damping and despinning method provides new solutions for the development of on-orbit capture technology.

Fault-tolerant feature-based estimation of space debris rotational motion during active removal missions

One of the key functionalities required by an Active Debris Removal mission is the assessment of the target kinematics and inertial properties. Passive sensors, such as stereo cameras, are often included in the onboard instrumentation of a chaser spacecraft for capturing sequential photographs and for tracking features of the target surface. A plenty of methods, based on Kalman filtering, are available for the estimation of the target's state from feature positions; however, to guarantee the filter convergence, they typically require continuity of measurements and the capability of tracking a fixed set of pre-defined features of the object. These requirements clash with the actual tracking conditions: failures in feature detection often occur and the assumption of having some a-priori knowledge about the shape of the target could be restrictive in certain cases. The aim of the presented work is to propose a fault-tolerant alternative method for estimating the angular velocity and the relative magnitudes of the principal moments of inertia of the target. Raw data regarding the positions of the tracked features are processed to evaluate corrupted values of a 3-dimentional parameter which entirely describes the finite screw motion of the debris and which primarily is invariant on the particular set of considered features of the object. Missing values of the parameter are completely restored exploiting the typical periodicity of the rotational motion of an uncontrolled satellite: compressed sensing techniques, typically adopted for recovering images or for prognostic applications, are herein used in a completely original fashion for retrieving a kinematic signal that appears sparse in the frequency domain. Due to its invariance about the features, no assumptions are needed about the target's shape and continuity of the tracking. The obtained signal is useful for the indirect evaluation of an attitude signal that feeds an unscented Kalman filter for the estimation of the global rotational state of the target. The results of the computer simulations showed a good robustness of the method and its potential applicability for general motion conditions of the target.

Dynamical analysis of a 2-degrees of freedom spatial pendulum

A spatial pendulum with the vertical immobile axis and horizontal mobile axis is studied and the differential equations of motion are obtained applying the method of Lagrange equations. The equations of motion were obtained for the general case; the only simplifying hypothesis consists in neglecting the principal moments of inertia about the axes normal to the oscillation axes. The system of nonlinear differential equations was numerically integrated. The correctness of the obtained solutions was corroborated to the dynamical simulation of the motion via dynamical analysis software. The perfect concordance between the two solutions proves the rightness of the equations obtained.

First low-frequency Einstein@Home all-sky search for continuous gravitational waves in Advanced LIGO data

We report results of a deep all-sky search for periodic gravitational waves from isolated neutron stars in data from the first Advanced LIGO observing run. This search investigates the low frequency range of Advanced LIGO data, between 20 and 100 Hz, much of which was not explored in initial LIGO. The search was made possible by the computing power provided by the volunteers of the Einstein@Home project. We find no significant signal candidate and set the most stringent upper limits to date on the amplitude of gravitational wave signals from the target population, corresponding to a sensitivity depth of 48.7 [1/$\sqrt{{\textrm{Hz}}}$]. At the frequency of best strain sensitivity, near 100 Hz, we set 90% confidence upper limits of $1.8 \times 10^{-25}$. At the low end of our frequency range, 20 Hz, we achieve upper limits of $3.9 \times 10^{-24}$. At 55 Hz we can exclude sources with ellipticities greater than $10^{-5}$ within 100 pc of Earth with fiducial value of the principal moment of inertia of $10^{38} \textrm{kg m}^2$.