scholarly journals The program «Moments of inertia» for calculating the moments of inertia of the rotational motion of molecules

2019 ◽  
Vol 57 (3) ◽  
pp. 42-50
Author(s):  
Mikhail N. Koverda ◽  
◽  
Eugeny N. Ofitserov ◽  
Anna A. Koverda ◽  
◽  
...  
Keyword(s):  
Rotational Motion ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Carbon Chain ◽  
Moment Of Inertia ◽  
Structure Property ◽  
Moments Of Inertia ◽  
Simple Molecules ◽  
The Moment

The moment of inertia of the rotational motion I, as a descriptor of the spatial structure of the molecule, which determines the properties of a substance, in accordance with the works of recent years, begins to acquire significance in the study of the «structure – property» dependencies, allowing one to describe the change in the properties of compounds in homologous series and address odd homologues. The problem is that there is no universal and transparent method for calculating the moments of inertia of the rotational motion of molecules. Researchers are trying to solve this problem in various ways: presenting the molecule as its carbon chain and calculating the moments of inertia only for it, neglecting the contribution of other atoms, manually calculating the moments of inertia for small simple molecules, based on their estimated geometry, extracting intermediate results from quantum chemical calculations of the program packages like Gaussian or Gamess. We have developed a program for the exact calculation of the moments of inertia, which uses the specification of the exact geometry of the molecule in three-dimensional space using Cartesian coordinates. The program is written on Perl programming language and is available under the GNU General Public License v3.0 (free software). The program uses XYZ files as input data. The principle of the program is to iteratively calculate the inertia moments for all possible positions in the space of the axis of rotation passing through the center of mass of the calculated molecule. The minimum and maximum values of the moments of inertia obtained during the calculation correspond to two perpendicular axes of rotation of the molecule (x and z). The moment of inertia with respect to the third remaining y axis is calculated after finding the canonical equation of the straight axis perpendicular to the found x and z axes.

New Theorems for Moments of Inertia

1993 ◽  
Vol 21 (4) ◽  
pp. 355-366 ◽  
Author(s):  
David L. Wallach
Keyword(s):  
Regular Polygon ◽  
Moment Of Inertia ◽  
Regular Polygons ◽  
Centre Of Mass ◽  
Moments Of Inertia ◽  
The Moment

The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.

Dynamics of a composite system in a point source-induced space–time

2021 ◽  
pp. 2150144
Author(s):  
Abdullah Guvendi
Keyword(s):  
Point Source ◽  
Composite System ◽  
Dimensional Space ◽  
Energy Levels ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Space Time ◽  
Spin Coupling ◽  
Quantum Oscillator ◽  
Dimensional Space Time

We investigate the dynamics of a composite system ([Formula: see text]) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By considering the interaction between the particles as Dirac oscillator coupling, we analyze the effects of space–time topology on the energy of such a [Formula: see text]. To achieve this, we solve the corresponding form of a two-body Dirac equation (fully-covariant) by assuming the center-of-mass of the particles is at rest and locates at the origin of the spatial geometry. Under this assumption, we arrive at a nonperturbative energy spectrum for the system in question. This spectrum includes spin coupling and depends on the angular deficit parameter [Formula: see text] of the geometric background. This provides a suitable basis to determine the effects of the geometric background on the energy of the [Formula: see text] under consideration. Our results show that such a [Formula: see text] behaves like a single quantum oscillator. Then, we analyze the alterations in the energy levels and discuss the limits of the obtained results. We show that the effects of the geometric background on each energy level are not same and there can be degeneracy in the energy levels for small values of the [Formula: see text].

scholarly journals Numerical Study of the Zero Velocity Surface and Transfer Trajectory of a Circular Restricted Five-Body Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
R. F. Wang ◽  
F. B. Gao
Keyword(s):  
Body Problem ◽  
Numerical Study ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Regular Tetrahedron ◽  
Transfer Trajectory ◽  
Zero Velocity ◽  
Zero Velocity Surfaces ◽  
Zero Velocity Surface

We focus on a type of circular restricted five-body problem in which four primaries with equal masses form a regular tetrahedron configuration and circulate uniformly around the center of mass of the system. The fifth particle, which can be regarded as a small celestial body or probe, obeys the law of gravity determined by the four primaries. The geometric configuration of zero-velocity surfaces of the fifth particle in the three-dimensional space is numerically simulated and addressed. Furthermore, a transfer trajectory of the fifth particle skimming over four primaries then is designed.

Increasing the Moment of Inertia of Crane Rails Torsional

2017 ◽  
Vol 865 ◽  
pp. 188-191
Author(s):  
Kirill Nezdanov ◽  
Igor Garkin ◽  
Nikolay Laskov
Keyword(s):  
Economic Benefits ◽  
Cross Sectional Area ◽  
Moment Of Inertia ◽  
High Moment ◽  
Operating Costs ◽  
Sectional Area ◽  
Cross Sectional ◽  
Moments Of Inertia ◽  
Section Profile ◽  
The Moment

This article is devoted to extreme increase in the moments of inertia of crane rails torsional strongly influence the endurance of crane girders. We investigate increase in moment of inertia of the rail under torsion with increasing thickness of the walls and shelves of thick-walled I-section profile in the square until its transformation into a square profile. It was found that the transformation of the profile of a monolithic solid square increases the moment of inertia of the torsion Jkr, cm4 to 3,1075 times and reaches its extreme. A cross-sectional area remains constant (const). Crane rails with a high moment of inertia for torsion provides significant economic benefits, and significantly reduces the operating costs of the enterprise.

The Inertial Effect in Rotational Fluorescence Depolarization

1992 ◽  
Vol 47 (9) ◽  
pp. 971-973 ◽  
Author(s):  
A. Kawski ◽  
P. Bojarski ◽  
A. Kubicki
Keyword(s):  
Empirical Equation ◽  
Molecular Geometry ◽  
Moment Of Inertia ◽  
Experimental Results ◽  
Inertial Effect ◽  
Fluorescence Depolarization ◽  
Moments Of Inertia ◽  
Low Viscosity ◽  
The Moment ◽  
Semi Empirical

Abstract The influence of the moment of inertia on the rotational fluorescence depolarization is discussed. Based on experimental results obtained for five luminescent compounds: 2,5-diphenyloxazole (PPO), 2,2'-p-phenylene-bis(5-phenyloxazole) (POPOP), p-bis[2-(5-α-naphthyloxazolyl)]-benzene (α-NOPON), 4-dimethylamino-ω-methylsulphonyl-trans-styrene (3a) in n-parafines at low viscosity (from 0.22 x 10-3 Pa • s to 0.993 x 10-3 Pa • s) and diphenylenestilbene (DPS) in different solvents, a semi-empirical equation is proposed, yielding moments of inertia that are only two to five times higher than those estimated from the molecular geometry

Dealing with varying moments of inertia of girders in bridge analysis

1988 ◽  
Vol 15 (2) ◽  
pp. 232-239 ◽  
Author(s):  
Baidar Bakht ◽  
Leslie G. Jaeger
Keyword(s):  
Load Distribution ◽  
Moment Of Inertia ◽  
Moments Of Inertia ◽  
Finite Strip ◽  
Girder Bridges ◽  
Grillage Analysis ◽  
Computer Based ◽  
Manual Methods ◽  
The Moment

In many slab-on-girder bridges, especially those that are continuous over two or more spans, the moment of inertia of a girder varies significantly along the length of the bridge. This paper critically examines the practice of analyzing such bridges for load distribution by methods that make the assumption of constant longitudinal torsional and flexural rigidities. It is found that this practice may not be valid for those slab-on-girder bridges in which variations of the girder moments of inertia are very large.A recommended procedure is given for cases in which the variation in moment of inertia is not too severe. The procedure involves (a) the determination of total bending moments, treating the bridge as a beam of variable moment of inertia, and (b) the determination of an equivalent constant moment of inertia for beams of varying moment of inertia. Using this procedure the load distribution properties of the bridge can be realistically analyzed by those computer-based methods (e.g., orthotropic plate, finite strip, and semicontinuum methods) or manual methods (e.g., AASHTO and Ontario methods) that cannot directly take account of the variation of longitudinal flexural rigidity.The validity of the recommended procedure is established by comparing its results with those of the grillage analysis method that does take account of the variation of the girder moment of inertia. Key words: bridge analysis, girders, load distribution, slab-on-girder bridges.

Making a pitch for the center of mass and the moment of inertia

1997 ◽  
Vol 65 (9) ◽  
pp. 903-907 ◽  
Author(s):  
W. N. Mei ◽  
Dan Wilkins
Keyword(s):  
Center Of Mass ◽  
Moment Of Inertia ◽  
The Moment

BIFURCATIONS FROM PLANAR TO THREE-DIMENSIONAL PERIODIC ORBITS IN THE RING PROBLEM OF N BODIES WITH RADIATING CENTRAL PRIMARY

2011 ◽  
Vol 21 (08) ◽  
pp. 2245-2260 ◽  
Author(s):  
T. J. KALVOURIDIS ◽  
K. G. HADJIFOTINOU
Keyword(s):  
Periodic Orbits ◽  
Periodic Motion ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Massless Particle ◽  
Critical Stability ◽  
Radiation Coefficient ◽  
Zero Velocity Surfaces ◽  
Three Dimensional Space

We consider the three-dimensional motion of a massless particle in a regular polygon formation of N primary bodies, one of which is located at the system's center of mass. Assuming that the central primary is a radiation source, we apply the simplified theory suggested by Radzievskii, in order to study the effect of radiation pressure in the three-dimensional dynamics of the system. We particularly study the evolution of the zero-velocity surfaces for various values of the radiation coefficient b0 and investigate also the cases with b0 > 1 (that is, radiation surpasses gravity) since for these cases, significant changes in the dynamics occur. We then locate numerically the onset of three-dimensional periodic motion from planar periodic motion by calculating the orbits' vertical critical stability. Many families of three-dimensional periodic motions are presented and the regions of the three-dimensional space where these motions take place, are determined. We subsequently investigate how the bifurcations from planar to three-dimensional periodic orbits are affected by the increase of the primary's radiation coefficient and how the overall dynamics of the system is affected by the value of the primaries' number N.

Trägheitsmomente nach Inglis und das Bohr-van-Leeuwensche Theorem

1960 ◽  
Vol 15 (5-6) ◽  
pp. 371-377
Author(s):  
Gerhart Lüders
Keyword(s):  
Rigid Rotation ◽  
Moment Of Inertia ◽  
Interacting Particles ◽  
Theoretical Determination ◽  
General Validity ◽  
Moments Of Inertia ◽  
Deformed Nuclei ◽  
The Moment

It has been stated by BOHR and MOTTELSON that INGLIS’ method for the theoretical determination of moments of inertia of deformed nuclei, in the limit of a great number of non-interacting particles leads to the moment of inertia of rigid rotation. Recently doubts have been raised regarding the general validity of this statement. In the present paper the proof of the assertion is given in detail and its relation to the BOHR-VAN-LEEUWEN theorem is discussed.

scholarly journals Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space

2021 ◽  
Vol 16 ◽  
pp. 73-84
Author(s):  
Maxim V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Fields ◽  
Characteristic Point ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Spatial Motion ◽  
Free Rigid Body

We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system

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