Finding Principal Axes of Complex Plane Rigid Body with Rending-Image of MATLAB

In order to find the principal axes of inertia and calculate their moment of inertia to any plane homogeneous rigid body for calculating easily the moment of inertia to any axis of this rigid body, the principal axes could be found and their moment of inertia could be calculated automatically by using the reading-image of MATLAB to read the image messages about the flat surface of the rigid body and by the procedures which ware made according to the logic relation about the principal axis and the moment of inertia of the rigid body. Applying this method in a homogeneous cube, a result was acquired, error of which is small compared with the theoretical value. So this method is reliable, convenient and practical

A teaching proposal for the study of Eigenvectors and Eigenvalues

Journal of Technology and Science Education ◽

10.3926/jotse.260 ◽

2017 ◽

Vol 7 (1) ◽

pp. 100 ◽

Author(s):

María José Beltrán Meneu ◽

Marina Murillo Arcila ◽

Enrique Jordá Mora

Keyword(s):

Rigid Body ◽

Mathematical Thinking ◽

Point Of View ◽

Moment Of Inertia ◽

Geometric Point ◽

The Moment ◽

Eigenvectors And Eigenvalues

In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students’ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

A semiclassical, microscopic model for nuclear collective rotation

Canadian Journal of Physics ◽

10.1139/p06-071 ◽

2006 ◽

Vol 84 (10) ◽

pp. 905-923 ◽

Author(s):

P Gulshani

Keyword(s):

Schrödinger Equation ◽

Time Reversal ◽

Schrodinger Equation ◽

Moment Of Inertia ◽

Time Dependent ◽

Microscopic Model ◽

Expectation Value ◽

Principal Axes ◽

Collective Rotation ◽

In this article, a semiclassical, microscopic model (dubbed SMRM) is derived to describe collective rotation in deformed nuclei. The SMRM is derived by transforming the time-dependent, multiparticle Schrodinger equation to a rotating frame whose axes are chosen to coincide with the principal axes of the expectation value of an arbitrary, second-rank, symmetric, tensor (nuclear shape) operator [Formula: see text]. This transformation circumvents the difficulty associated with the introduction of redundant particle coordinates in the Villars' transformation. The SMRM Schrodinger equation, which resembles the cranking model (CM) equation, is a time-dependent, time-reversal-invariant, nonlinear integro-differential equation. In this equation, the angular velocity is determined by the wave function and deformation–rotation shear operators, and this introduces the nonlinearity in the equation. A variational method is proposed and justified to obtain: a stationary solution of the SMRM Schrodinger equation in the Rayleigh–Ritz Hartree–Fock particle–hole formalism, the rotational energy increment, and the associated moment of inertia. When exchange interaction terms are neglected or a separable interaction is used, the SMRM moment of inertia is shown to reduce to that given by the CM provided that a certain relationship exists between the moment of inertia and the expectation value of [Formula: see text]. However, the SMRM and CM wave functions are not the same (SMRM preserves and CM violates time-reversal invariance) implying that the calculated values of other parameters, including the moment of inertia at higher values of the angular momentum, may not be the same in the two models. In any case, the SMRM derives the CM moment of inertia from a microscopic, time-reversal invariant, nonlinear theory.PACS Nos.: 21.60.Ev, 21.60.Fw, 21.60.Jz

R fluids

Serbian Astronomical Journal ◽

10.2298/saj0876023c ◽

2008 ◽

pp. 23-35 ◽

Author(s):

R. Caimmi

Keyword(s):

Kinetic Energy ◽

Velocity Component ◽

Axial Velocity ◽

Tangential Velocity ◽

Random Motion ◽

Moment Of Inertia ◽

Random Velocity ◽

Principal Axes ◽

The Moment ◽

Figure Rotation

A theory of collisionless fluids is developed in a unified picture, where nonrotating (?f1 = ?f2 = ?f3 = 0) figures with some given random velocity component distributions, and rotating (?f1 = ?f2 = ?f3 ) figures with a different random velocity component distributions, make adjoint configurations to the same system. R fluids are defined as ideal, self-gravitating fluids satisfying the virial theorem assumptions, in presence of systematic rotation around each of the principal axes of inertia. To this aim, mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The figure rotation is defined as the mean angular velocity, weighted on the moment of inertia, with respect to a selected axis. The generalized tensor virial equations (Caimmi and Marmo 2005) are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general hypotheses, by reversing the sign of tangential or axial velocity components of an assigned fraction of particles, leaving the distribution function and other parameters unchanged (Meza 2002). The application of the reversion process to tangential velocity components is found to imply the conversion of random motion rotation kinetic energy into systematic motion rotation kinetic energy. The application of the reversion process to axial velocity components is found to imply the conversion of random motion translation kinetic energy into systematic motion translation kinetic energy, and the loss related to a change of reference frame is expressed in terms of systematic motion (imaginary) rotation kinetic energy. A number of special situations are investigated in greater detail. It is found that an R fluid always admits an adjoint configuration where figure rotation occurs around only one principal axis of inertia (R3 fluid), which implies that all the results related to R3 fluids (Caimmi 2007) may be ex- tended to R fluids. Finally, a procedure is sketched for deriving the spin parameter distribution (including imaginary rotation) from a sample of observed or simulated large-scale collisionless fluids i.e. galaxies and galaxy clusters.

Un análisis biomecánico de la patada descendente de taekwondo modificada

Revista de Artes Marciales Asiáticas ◽

10.18002/rama.v2i1.282 ◽

2012 ◽

Vol 2 (1) ◽

pp. 28

Author(s):

Luigi T. Bercades ◽

Willy Pieter

Keyword(s):

Angular Momentum ◽

Theoretical Analysis ◽

Rigid Body ◽

Moment Of Inertia ◽

Font Size ◽

Alternate Version ◽

This study is a theoretical analysis of the kinematic and kinetic aspects of the modified taekwondo axe kick. The traditional or classical axe kick has the whole kicking leg (the thigh and the shank) considered as a rigid body on both the upswing and downswing phases of the kick, which is speculated to have sufficient angular momentum to increase the risk of some forms of injuries in competition. The present study seeks to present an alternate version that will decrease the moment of inertia on the downswing, reduce the subsequent angular momentum, and finally decrease the resultant impulse to the target. Theoretically, this will reduce the chances of certain types of injury caused by the kick.

Influence of the Moment of Inertia of Rigid Body CPVA on the Vibration Suppression Effect

The Proceedings of the Dynamics & Design Conference ◽

10.1299/jsmedmc.2019.140 ◽

2019 ◽

Vol 2019 (0) ◽

pp. 140

Author(s):

Ryota OKUMURA ◽

Shota YABUI ◽

Tsuyoshi INOUE

Keyword(s):

Rigid Body ◽

Vibration Suppression ◽

Moment Of Inertia ◽

Suppression Effect ◽

STUDY ON THE MECHANICS PROPERTY OF THREE DEGREES OF FREEDOM AIR-BEARING TESTBED--INFLUENCE ON THE MOMENT OF INERTIA MATRIX AND ON THE DIRECTION OF INERTIA PRINCIPAL AXIS WHEN ACTED ON GRAVITY

Journal of Mechanical Engineering ◽

10.3901/jme.2006.04.191 ◽

2006 ◽

Vol 42 (04) ◽

pp. 191 ◽

Author(s):

Yanbin LI

Keyword(s):

Degrees Of Freedom ◽

Principal Axis ◽

Moment Of Inertia ◽

Air Bearing ◽

Inertia Matrix ◽

The Moment ◽

Three Degrees Of Freedom

Polarization Navigation Simulation System and Skylight Compass Method Design Based upon Moment of Inertia

Mathematical Problems in Engineering ◽

10.1155/2020/4081269 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Huaju Liang ◽

Hongyang Bai ◽

Ning Liu ◽

Xiubao Sui

Keyword(s):

Rigid Body ◽

Extreme Values ◽

Rigid Body Dynamics ◽

Moment Of Inertia ◽

Atmospheric Scattering ◽

Skylight Polarization ◽

Polarization Image ◽

Simulation And Experiment ◽

The Moment ◽

Research Studies

Unpolarized sunlight becomes polarized by atmospheric scattering and produces a skylight polarization pattern in the sky, which is detected for navigation by several species of insects. Inspired by these insects, a growing number of research studies have been conducted on how to effectively determine a heading angle from polarization patterns of skylight. However, few research studies have considered that the pixels of a pixelated polarization camera can be easily disturbed by noise and numerical values among adjacent pixels are discontinuous caused by crosstalk. So, this paper proposes a skylight compass method based upon the moment of inertia (MOI). Inspired by rigid body dynamics, the MOI of a rigid body with uniform mass distribution reaches the extreme values when the rigid body rotates on its symmetry axes. So, a whole polarization image is regarded as a rigid body. Then, orientation determination is transformed into solving the extreme value of MOI. This method makes full use of the polarization information of a whole polarization image and accordingly reduces the influence of the numerical discontinuity among adjacent pixels and measurement noise. In addition, this has been verified by numerical simulation and experiment. And the compass error of the MOI method is less than 0.44° for an actual polarization image.