scholarly journals General-relativistic equations of motion in terms of energy and angular momentum

2003 ◽  
Vol 24 (4) ◽  
pp. 413-417 ◽  
Author(s):  
Yong Gwan Yi
Keyword(s):  
Angular Momentum ◽  
Equations Of Motion ◽  
General Relativistic ◽  
Relativistic Equations

scholarly journals A GRAVITOMAGNETIC EFFECT ON THE ORBIT OF A TEST BODY DUE TO THE EARTH'S VARIABLE ANGULAR MOMENTUM

2002 ◽  
Vol 11 (05) ◽  
pp. 781-787 ◽  
Author(s):  
LORENZO IORIO
Keyword(s):  
Angular Momentum ◽  
Test Particle ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Slow Motion ◽  
Weak Field ◽  
Test Body ◽  
Angular Velocity Vector ◽  
Motion Approximation ◽  
General Relativistic

The well known general relativistic Lense–Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effect of the variation in time of the central body's angular momentum on the orbit of a test mass is considered. It can be shown that it is analogue to the inertial acceleration due to the time derivative of the angular velocity vector of an accelerated frame. The possibility of detecting such effect in the gravitational field of the Earth with LAGEOS-like satellites is investigated. It turns out that the orbital effects are far too small to be measured.

scholarly journals A Post-Newtonian Gravitomagnetic Effect on the Orbital Motion of a Test Particle around Its Primary Induced by the Spin of a Distant Third Body

Universe ◽  
2019 ◽  
Vol 5 (4) ◽  
pp. 87
Author(s):  
Lorenzo Iorio
Keyword(s):  
Angular Momentum ◽  
Test Particle ◽  
Equations Of Motion ◽  
Body System ◽  
Long Term Effects ◽  
Body Effect ◽  
Angular Momenta ◽  
General Relativistic ◽  
Range Rate

We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum S X of a rotating mass M X orbited at distance r X by a local gravitationally bound restricted two-body system S of size r ≪ r X consisting of a test particle revolving around a massive body M. At the lowest post-Newtonian order, we analytically work out the doubly averaged rates of change of the Keplerian orbital elements of the test particle by finding non-vanishing long-term effects for the inclination I, the node Ω and the pericenter ω . Such theoretical results are confirmed by a numerical integration of the equations of motion for a fictitious 3-body system. We numerically calculate the magnitudes of the post-Newtonian gravitomagnetic 3-body precessions for some astronomical scenarios in our solar system. For putative man-made orbiters of the natural moons Enceladus and Europa in the external fields of Saturn and Jupiter, the relativistic precessions due to the angular momenta of the gaseous giant planets can be as large as ≃10 − 50 milliarcseconds per year (mas year−1). A preliminary numerical simulation shows that, for certain orbital configurations of a hypothetical Europa orbiter, its range-rate signal Δ ρ ˙ can become larger than the current Doppler accuracy of the existing spacecraft Juno at Jupiter, i.e., σ ρ ˙ = 0.015 mm s−1, after 1 d. The effects induced by the Sun’s angular momentum on artificial probes of Mercury and the Earth are at the level of ≃ 1 − 0.1 microarcseconds per year (μas year −1).

scholarly journals A New General Covariant Approach to the General Relativistic Two-Body Problem

1974 ◽  
Vol 64 ◽  
pp. 102-102
Author(s):  
Arnold Rosenblum
Keyword(s):  
Gravitational Radiation ◽  
Body Problem ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Covariant Approach ◽  
Two Body Problem ◽  
General Relativistic ◽  
Present Understanding ◽  
Relativistic Equations

A new general covariant approach to the general relativistic equations of motion is presented. It is stressed that our present understanding of the development of binaries due to general relativistic effects and of the power emitted by these systems in the form of gravitational radiation is highly unsatisfactory.

scholarly journals The general relativistic Poynting–Robertson effect: II. A photon flux with nonzero angular momentum

2011 ◽  
Vol 28 (3) ◽  
pp. 035008 ◽  
Author(s):  
Donato Bini ◽  
Andrea Geralico ◽  
Robert T Jantzen ◽  
Oldřich Semerák ◽  
Luigi Stella
Keyword(s):  
Angular Momentum ◽  
Photon Flux ◽  
General Relativistic

Ion acceleration by multiple laser pulses and their spontaneous electromagnetic fields in plasma

2008 ◽  
Vol 74 (1) ◽  
pp. 111-118
Author(s):  
FEN-CE CHEN
Keyword(s):  
Magnetic Fields ◽  
Electric Field ◽  
Analytical Model ◽  
Electromagnetic Fields ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Laser Pulses ◽  
The Self ◽  
Electric And Magnetic Fields ◽  
Relativistic Equations

AbstractThe acceleration of ions by multiple laser pulses and their spontaneously generated electric and magnetic fields is investigated by using an analytical model for the latter. The relativistic equations of motion of test charged particles are solved numerically. It is found that the self-generated axial electric field plays an important role in the acceleration, and the energy of heavy test ions can reach several gigaelectronvolts.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

AN ACTION PRINCIPLE FOR MAGNETOHYDRODYNAMICS

1963 ◽  
Vol 41 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
M. G. Calkin
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Induction ◽  
Vector Potential ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Action Principle ◽  
Invariance Properties ◽  
Conservation Of Momentum

The equations of motion of an inviscid, infinitely conducting fluid in an electromagnetic field are transformed into a form suitable for an action principle. An action principle from which these equations may be derived is found. The conservation laws follow from invariance properties of the action. The space–time invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Helmholtz vortex theorem of hydrodyanmics, and the conservation of the volume integrals of A∙B and v∙B, where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.

Orbital dynamics of the gravitational field of stringy black holes

2014 ◽  
Vol 29 (29) ◽  
pp. 1450144 ◽  
Author(s):  
Yu Zhang ◽  
Jin-Ling Geng ◽  
En-Kun Li
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Gravitational Field ◽  
Phase Plane ◽  
Equations Of Motion ◽  
Orbital Dynamics ◽  
Phase Plane Analysis ◽  
Test Particles ◽  
Stable Circular Orbit ◽  
The Stability

In this paper, we study the orbital dynamics of the gravitational field of stringy black holes by analyzing the effective potential and the phase plane diagram. By solving the equation of Lagrangian, the general relativistic equations of motion in the gravitational field of stringy black holes are given. It is easy to find that the motion of test particles depends on the energy and angular momentum of the test particles. Using the phase plane analysis method and combining the conditions of the stability, we discuss different types of the test particles' orbits in the gravitational field of stringy black holes. We get the innermost stable circular orbit which occurs at r min = 5.47422 and when the angular momentum b ≤ 4.3887 the test particles will fall into the black hole.

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.

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