Equations of motion of compact binaries at the third post-Newtonian order

Pramana ◽  
2004 ◽  
Vol 63 (4) ◽  
pp. 685-701
Author(s):  
Luc Blanchet
Keyword(s):  
Equations Of Motion ◽  
Compact Binaries ◽  
The Third

scholarly journals Relativistic equations of motion of massive bodies

2009 ◽  
Vol 5 (S261) ◽  
pp. 102-102
Author(s):  
Luc Blanchet
Keyword(s):  
Gravitational Radiation ◽  
State Of The Art ◽  
Equations Of Motion ◽  
Speed Of Light ◽  
Black Hole Binaries ◽  
Compact Binaries ◽  
The Third ◽  
Current State ◽  
Relativistic Equations ◽  
Equations Of Motions

AbstractHighly relativistic equations of motions will play a crucial role for the detection and analysis of gravitational waves emitted by inspiralling compact binaries in detectors LIGO/VIRGO on ground and LISA in space. Indeed these very relativistic systems (with orbital velocities of the order of half the speed of light in the last orbital rotations) require the application of a high-order post-Newtonian formalism in general relativity for accurate description of their motion and gravitational radiation [1]. In this contribution the current state of the art which has reached the third post-Newtonian approximation for the equations of motion [2–6] and gravitational waveform [7–9] has been described (see [10] for an exhaustive review). We have also emphasized the successful matching of the post-Newtonian templates to numerically generated predictions for the merger and ring-down in the case of black-hole binaries [11].

scholarly journals The third way to 3D gravity

2015 ◽  
Vol 24 (12) ◽  
pp. 1544015 ◽  
Author(s):  
Eric Bergshoeff ◽  
Wout Merbis ◽  
Alasdair J. Routh ◽  
Paul K. Townsend
Keyword(s):  
Equations Of Motion ◽  
Massive Gravity ◽  
De Sitter ◽  
Gravitational Field Equation ◽  
Third Way ◽  
Metric Tensor ◽  
The Third ◽  
Higher Dimensional ◽  
Conservation Condition ◽  
3D Gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers

1991 ◽  
Author(s):  
Keith W. Buffinton
Keyword(s):  
Floquet Theory ◽  
Equations Of Motion ◽  
Perturbation Techniques ◽  
Axial Motion ◽  
The Third ◽  
Straightforward Application ◽  
Method Yield ◽  
Robotic Devices ◽  
Axially Moving

Abstract Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.

scholarly journals Virgo and Gravitational-Wave Computing in Europe

2020 ◽  
Vol 245 ◽  
pp. 07050
Author(s):  
Stefano Bagnasco
Keyword(s):  
Gravitational Wave ◽  
Current Status ◽  
Low Latency ◽  
Observational Period ◽  
Compact Binaries ◽  
The Third ◽  
Compact Binary ◽  
Continuous Waves ◽  
The Us ◽  
Wave Event

Advanced Virgo is an interferometer for the detection of gravitational waves at the European Gravitational Observatory in Italy. Along with the two Advanced LIGO interferometers in the US, Advanced Virgo is being used to collect data from astrophysical sources such as compact binary coalescences and is currently running the third observational period, collecting gravitational wave event candidates at a rate of more than once per week. Data from the interferometer are processed by running search pipelines for several expected signals, from coalescing compact binaries to continuous waves and burst events. Furthermore, detector characterisation studies are run. Some of the processing needs to be done with low latency, to be able to provide triggers for other observatories and make multi-messenger observations possible. Deep searches are run offline on external computing centres. Thus, data needs also to be reliably and promptly distributed from the EGO site to computer centres in Europe and the US for further analysis and archival storage. Two of the defining characteristics of Virgo computing are the heterogeneity of the activities and the need to interoperate with LIGO. A very wide array of analysis pipelines differing in scientific target, implementation details and running environment assumptions have to be allowed to run ubiquitously and uniformly on dedicated resources and, in perspective, on heterogeneous infrastructures. The current status, possible strategies and outlook of Virgo computing are discussed.

Radial component of vortex electric field force

2021 ◽  
Vol 11 (1) ◽  
pp. 32-35
Author(s):  
Vasyl Tchaban ◽  
Keyword(s):  
Electric Field ◽  
Equations Of Motion ◽  
Spherical Body ◽  
Radial Component ◽  
Force Interaction ◽  
Finite Speed ◽  
The Third ◽  
Electric Field Force ◽  
Electrically Charged ◽  
Positively Charged

he differential equations of motion of electrically charged bodies in an uneven vortex electric field at all possible range of velocities are obtained in the article. In the force interaction, in addition to the two components – the Coulomb and Lorentz forces – the third component of a hitherto unknown force is involved. This component turned out to play a crucial role in the dynamics of movement. The equations are written in the usual 3D Euclidean space and physical time.This takes into account the finite speed of electric field propagation and the law of electric charge conservation. On this basis, the trajectory of the electron in an uneven electric field generated by a positively charged spherical body is simulated. The equations of motion are written in vector and coordinate forms. A physical interpretation of the obtained mathematical results is given. Examples of simulations are given.

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.

Sign in / Sign up

Export Citation Format

Share Document