Angular Momentum Equation

2019 ◽  
pp. 113-126
Author(s):  
Osamu Morita
Keyword(s):  
Angular Momentum ◽  
Momentum Equation

Comparison between Analytical and Vectorial Methods of the Synthesis of Equations of Motion

1983 ◽  
Vol 197 (4) ◽  
pp. 265-274
Author(s):  
Z J Goraj
Keyword(s):  
Angular Momentum ◽  
Analytical Method ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Discrete Systems ◽  
Momentum Equation ◽  
Lagrange Equations ◽  
Weak Points ◽  
Complicated Geometry ◽  
Boltzmann Hamel Equations

In this paper the advantages and weak points of the analytical and vectorial methods of the derivation of equations of motion for discrete systems are considered. The analytical method is discussed especially with respect to Boltzmann-Hamel equations, as generalized Lagrange equations. The vectorial method is analysed with respect to the momentum equation and to the generalized angular momentum equation about an arbitrary reference point, moving in an arbitrary manner. It is concluded that, for the systems with complicated geometry of motion and a large number of degrees of freedom, the vectorial method can be more effective than the analytical method. The combination of the analytical and vectorial methods helps to verify the equations of motion and to avoid errors, especially in the case of systems with rather complicated geometry.

scholarly journals Transonic accretion and winds around Pseudo-Kerr black holes andcomparison with general relativistic solutions

2022 ◽  
Author(s):  
Abhrajit Bhattacharjee ◽  
Sandip Kumar Chakrabarti ◽  
Dipak Debnath
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Time Scale ◽  
Momentum Equation ◽  
Accretion Flows ◽  
Timing Properties ◽  
Surrounding Space ◽  
General Relativistic ◽  
Corotating Frame

Abstract Spectral and timing properties of accretion flows on a black hole depend on their density and temperature distributions, which, in turn come from the underlying dynamics. Thus, an accurate description of the flow which includes hydrodynamics and radiative transfer is a must to interpret the observational results. In the case of non-rotating black holes, Pseudo- Newtonian description of surrounding space-time enables one to make a significant progress in predicting spectral and timing properties. This formalism is lacking for the spinning black holes. In this paper, we show that there exists an exact form of ‘natural’ potential derivable from the general relativistic (GR) radial momentum equation written in the local corotating frame. Use of this potential in an otherwise Newtonian set of equations, allows us to describe transonic flows very accurately as is evidenced by comparing with solutions obtained from the full GR framework. We study the properties of the sonic points and the centrifugal pressure supported shocks in the parameter space spanned by the specific energy and the angular momentum, and compare with the results of GR hydrodynamics. We show that this potential can safely be used for the entire range of Kerr parameter −1 < a < 1 for modeling of observational results around spinning black holes. We assume the flow to be inviscid. Thus, it is non-dissipative with constant energy and angular momentum. These assumptions are valid very close to the black hole horizon as the infall time scale is much shorter as compared to the viscous time scale.

Simulations of Magnetoviscosity of Dilute Suspensions of Magnetic Ellipsoids

2008 ◽  
Author(s):  
J. H. Sa´nchez ◽  
C. Rinaldi
Keyword(s):  
Brownian Motion ◽  
Angular Momentum ◽  
Momentum Equation ◽  
Orientation Space ◽  
Fluctuation Dissipation ◽  
Ellipsoidal Particles ◽  
Fluctuation Dissipation Theorem ◽  
Dilute Suspensions ◽  
Dilute Suspension ◽  
Rotational Brownian Motion

We studied the rotational Brownian motion of magnetic triaxial ellipsoidal particles (orthotropic particles) suspended in a Newtonian fluid, in the dilute suspension limit, under applied shear and magnetic fields. The algorithm describing the change in the particle magnetization has been derived from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Results are presented for the response of dilute suspensions of ellipsoidal particles to constant magnetic and shear flow fields.

Hydrogen-like Atoms

2020 ◽  
pp. 328-339
Author(s):  
Jochen Autschbach
Keyword(s):  
Organic Chemistry ◽  
Fixed Point ◽  
Angular Momentum ◽  
Hydrogen Atom ◽  
Total Energy ◽  
Bound States ◽  
Principal Quantum Number ◽  
Momentum Equation ◽  
Polar Coordinates ◽  
Real Linear

This chapter shows how the electronic Schrodinger equation (SE) is solved for a hydrogen-like atom, i.e. an electron moving in the field of a fixed point-like nucleus with charge number Z. The hydrogen atom corresponds to Z = 1. The potential in atomic units is –Z/r, with r being the distance of the electron from the nucleus. The SE is not separable in Cartesian coordinates, but in spherical polar coordinates it separates into a radial equation and an angular momentum equation. The bound states have a total energy of –Z2/(2n2), with n = nr + ℓ being the principal quantum number (q.n.), ℓ = 0,1,2,… the angular momentum q.n., and nr = 1,2,3,… being a radial q.n. Each state for a given ℓ is 2ℓ+1-fold degenerate, with the components labelled by the projection q.n. mℓ. The wavefunctions for mℓ ≠ 0 are complex, but real linear combinations can be formed. This gives the atomic orbitals known from general and organic chemistry. Different ways of visualizing the real wavefunctions are discussed, e.g. as iso-surfaces.

scholarly journals Toward Understanding the Dynamics of Spinup in Emanuel’s Tropical Cyclone Model

2019 ◽  
Vol 76 (10) ◽  
pp. 3089-3093 ◽  
Author(s):  
Michael T. Montgomery ◽  
Roger K. Smith
Keyword(s):  
Angular Momentum ◽  
Tropical Cyclone ◽  
Turbulent Mixing ◽  
First Principles ◽  
Momentum Equation ◽  
Friction Layer ◽  
Tangential Wind ◽  
Low Levels ◽  
The Absolute

Abstract We seek to understand the mechanism of vortex spinup in Emanuel’s 2012 axisymmetric theory for tropical cyclone intensification in physical coordinates, starting from first principles. It is noted that, while spinup of the maximum tangential wind must occur at low levels, within or at the top of the friction layer, this spinup is unconstrained by a radial momentum equation in this layer. Instead, the spinup is controlled by a parameterization of turbulent mixing in the upper-tropospheric outflow layer, which, as is shown, determines indirectly the rate of inward movement of the absolute angular momentum surfaces. Nevertheless, the physics of how upper-tropospheric mixing leads to spinup in or at the top of the friction layer are unclear and, as discussed, may be irrelevant to spinup in the model.

scholarly journals Magnetic wind-driven accretion in dwarf novae

2019 ◽  
Vol 626 ◽  
pp. A116 ◽  
Author(s):  
Nicolas Scepi ◽  
Guillaume Dubus ◽  
Geoffroy Lesur
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Turbulent Transport ◽  
Momentum Equation ◽  
Light Curves ◽  
Rotational Instability ◽  
Dwarf Novae ◽  
X Ray ◽  
The Impact ◽  
X Ray Binaries

Context. Dwarf novae (DNe) and X-ray binaries exhibit outbursts thought to be due to a thermal-viscous instability in the accretion disk. The disk instability model (DIM) assumes that accretion is driven by turbulent transport, customarily attributed to the magneto-rotational instability (MRI). However, recent results point out that MRI turbulence alone fails to reproduce the light curves of DNe. Aims. Our aim is to study the impact of wind-driven accretion on the light curves of DNe. Local and global simulations show that magneto-hydrodynamic winds are present when a magnetic field threads the disk, even for relatively high ratios of thermal pressure to magnetic pressure (β ≈ 105). These winds are very efficient in removing angular momentum but do not heat the disk, thus they do not behave as MRI-driven turbulence. Methods. We add the effect of wind-driven magnetic braking in the angular momentum equation of the DIM but neglect the mass loss due to the wind. We assume a fixed magnetic configuration: dipolar or constant with radius. We use prescriptions for the wind torque and the turbulent torque derived from shearing box simulations. Results. The wind torque enhances the accretion of matter, resulting in light curves that look like DNe outbursts when assuming a dipolar field with a moment μ ≈ 1030 G cm3. In the region where the wind torque dominates the disk is cold and optically thin, and the accretion speed is super-sonic. The inner disk behaves as if truncated, leading to higher quiescent X-ray luminosities from the white dwarf boundary layer than expected with the standard DIM. The disk is stabilized if the wind-dominated region is large enough, potentially leading to “dark” disks that emitting little radiation. Conclusion. Wind-driven accretion can play a key role in shaping the light curves of DNe and X-ray binaries. Future studies will need to include the time evolution of the magnetic field threading the disk to fully assess its impact on the dynamics of the accretion flow.

The angular momentum equation for a finite element of a fluid: A new representation and application to turbulent modeling

2002 ◽  
Vol 14 (8) ◽  
pp. 2673-2682 ◽  
Author(s):  
M. Iovieno ◽  
D. Tordella
Keyword(s):  
Finite Element ◽  
Angular Momentum ◽  
Momentum Equation ◽  
Turbulent Modeling

scholarly journals Vibrational effect on unidirectional time-dependent angular momentum in low-symmetry aromatic ring molecule induced by two linearly polarized UV laser

2019 ◽  
Vol 16 (6) ◽  
pp. 62
Author(s):  
La Dung Kiet ◽  
Hirobumi Mineo
Keyword(s):  
Angular Momentum ◽  
Aromatic Ring ◽  
Theoretical Study ◽  
Momentum Equation ◽  
Time Dependent ◽  
Uv Laser ◽  
Toluene Molecule ◽  
Linearly Polarized ◽  
Low Symmetry

In this study, we present the results of a theoretical study of the time-dependent angular momentum equation for low-symmetry aromatic ring molecule combine with vibrational effect using two linearly polarized UV laser. We consider the vibrational effect on Toluene molecule and show how the vibrational effect to change of the oscillation periods of unidirectional angular momentum.

scholarly journals A comparative study of quaternionic rotational Dirac equation and its interpretation

2020 ◽  
Vol 17 (02) ◽  
pp. 2050018 ◽  
Author(s):  
B. C. Chanyal ◽  
Sandhya Karnatak
Keyword(s):  
Angular Momentum ◽  
Dirac Equation ◽  
Rest Mass ◽  
Momentum Equation ◽  
Rotational Frequency ◽  
Rotational Energy ◽  
Relativistic Mass ◽  
Mass Moment ◽  
Rotational Momentum ◽  
Mass Moment Of Inertia

In this study, we develop the generalized Dirac-like four-momentum equation for rotating spin-1/2 particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists of the rotational energy and angular momentum of particle and antiparticle. Accordingly, we also discuss the four-vector form of quaternionic relativistic mass, moment of inertia and rotational energy-momentum in Euclidean space-time. The quaternionic four-angular momentum, (i.e. the rotational analogy of four-linear momentum) predicts the dual energy (rest mass energy and pure rotational energy) and dual momentum (linear-like momentum and pure rotational momentum). Further, the solutions of quaternionic rotational Dirac energy-momentum are obtained by using one-, two- and four-component of quaternionic spinor. We also demonstrate the solutions of quaternionic plane wave equation which gives the rotational frequency and wave propagation vector of Dirac particles and antiparticles in terms of quaternionic form.

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