scholarly journals A relativistic motion integrator: numerical accuracy and illustration with BepiColombo and Mars-NEXT

2009 ◽  
Vol 5 (S261) ◽  
pp. 144-146 ◽  
Author(s):  
A. Hees ◽  
S. Pireaux
Keyword(s):  
Numerical Study ◽  
Equations Of Motion ◽  
Relativistic Motion ◽  
Numerical Accuracy ◽  
Relativistic Corrections ◽  
Relativistic Equations

AbstractToday, the motion of spacecraft is still described by the classical Newtonian equations of motion plus some relativistic corrections. This approach might become cumbersome due to the increasing precision required. We use the Relativistic Motion Integrator (RMI) approach to numerically integrate the native relativistic equations of motion for a spacecraft. The principle of RMI is presented. We compare the results obtained with the RMI method with those from the usual Newton plus correction approach for the orbit of the BepiColombo (around Mercury) and Mars-NEXT (around Mars) orbiters. Finally, we present a numerical study of RMI and we show that the RMI approach is relevant to study the orbit of spacecraft.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

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.

scholarly journals New Results on the Motions of Asteroids in Resonances

1992 ◽  
Vol 152 ◽  
pp. 145-152 ◽  
Author(s):  
R. Dvorak
Keyword(s):  
Initial Conditions ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Close Approach ◽  
Integration Time ◽  
Time Interval ◽  
Time Intervals ◽  
3 Dimensional ◽  
Special Cases ◽  
Good Agreement

In this article we present a numerical study of the motion of asteroids in the 2:1 and 3:1 resonance with Jupiter. We integrated the equations of motion of the elliptic restricted 3-body problem for a great number of initial conditions within this 2 resonances for a time interval of 104 periods and for special cases even longer (which corresponds in the the Sun-Jupiter system to time intervals up to 106 years). We present our results in the form of 3-dimensional diagrams (initial a versus initial e, and in the z-axes the highest value of the eccentricity during the whole integration time). In the 3:1 resonance an eccentricity higher than 0.3 can lead to a close approach to Mars and hence to an escape from the resonance. Asteroids in the 2:1 resonance with Jupiter with eccentricities higher than 0.5 suffer from possible close approaches to Jupiter itself and then again this leads in general to an escape from the resonance. In both resonances we found possible regions of escape (chaotic regions), but only for initial eccentricities e > 0.15. The comparison with recent results show quite a good agreement for the structure of the 3:1 resonance. For motions in the 2:1 resonance our numeric results are in contradiction to others: high eccentric orbits are also found which may lead to escapes and consequently to a depletion of this resonant regions.

scholarly journals Electron acceleration in underdense plasmas described with a classical effective theory

2015 ◽  
Vol 33 (2) ◽  
pp. 307-313 ◽  
Author(s):  
M. A. Pocsai ◽  
S. Varró ◽  
I. F. Barna
Keyword(s):  
Experimental Data ◽  
Continuous Medium ◽  
Equations Of Motion ◽  
Electron Acceleration ◽  
Index Of Refraction ◽  
Effective Theory ◽  
Electron Motion ◽  
Particle In Cell ◽  
Underdense Plasmas ◽  
Relativistic Equations

AbstractAn effective theory of laser–plasma-based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction nm in which a single electron propagates. Because of the simplicity of this model, we did not perform particle-in-cell (PIC) simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analyzed. We compared our results with PIC simulations and experimental data.

A Numerical Study on the Effect of Unbalance and Misalignment Fault Parameters in a Rigid Rotor Levitated by Active Magnetic Bearings

2019 ◽  
Author(s):  
Prabhat Kumar ◽  
Rajiv Tiwari
Keyword(s):  
Numerical Study ◽  
Equations Of Motion ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Inertia Force ◽  
Dimensional System ◽  
Rigid Rotor ◽  
Active Magnetic Bearings ◽  
Fault Parameters ◽  
Misalignment Fault

Abstract This paper focusses on analysing the vibration behaviour of a rigid rotor levitated by active magnetic bearings (AMB) under the influence of unbalance and misalignment parameters. Unbalance in rotor and misalignment between rotor and both supported AMBs are key fault parameters in the rotor system. To demonstrate this dynamic analysis, an unbalanced rigid rotor with a disc at the middle levitated by two misaligned active magnetic bearings has been mathematically modelled. One of the novel concepts is also described as how the force due to active magnetic bearings on the rigid rotor is modified when the rotor is parallel misaligned with AMBs. With inclusion of inertia force, unbalance force and force due to misaligned AMBs, the equations of motion of the rigid rotor system are derived and converted into dimensionless form in terms of various non-dimensional system and fault parameters. Numerical simulations have been performed to yield the dimensionless rotor displacement and controlling current responses at AMBs. The prime intention of the present paper is to study the effect on the displacement response of the rigid rotor system and the current consumption of AMBs for different ranges of disc eccentricities and rotor-AMB misalignments.

scholarly journals The spinless relativistic Hellmann problem

2019 ◽  
Vol 34 (05) ◽  
pp. 1950028
Author(s):  
Wolfgang Lucha ◽  
Franz F. Schöberl
Keyword(s):  
Coulomb Potential ◽  
Bound States ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Kinetic Term ◽  
Discrete Eigenvalue ◽  
Hellmann Potential ◽  
Relativistic Equations

We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb potential and an either attractive or repulsive Yukawa potential and, hence, generalizations of the Hellmann potential employed in several areas of science. These insights should provide useful guidelines to all attempts of finding appropriate descriptions of bound states by (semi-)relativistic equations of motion.

The Vibrations of the Engine with Neo-Hookean Suspension

2013 ◽  
Vol 430 ◽  
pp. 53-59 ◽  
Author(s):  
Nicolae Doru Stanescu ◽  
Dinel Popa
Keyword(s):  
Degrees Of Freedom ◽  
Stable Equilibrium ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Harmonic Force ◽  
Small Oscillations ◽  
Excited System ◽  
Beat Phenomenon ◽  
Three Degrees Of Freedom

Our paper realizes a study of the vibrations of an engine excited by a harmonic force and sustained by four identical neo-Hookean springs of negligible masses. The considered model is one with three degrees of freedom (one translation and two rotations) and we obtain for it the equations of motion. Using these equations, we determine for the unexcited system the equilibrium positions and their stability. We also study the small oscillations about the stable equilibrium positions and we find the fundamental eigenpulsations of the system. For the case of the excited system we perform a numerical study considering the situation when the pulsation of the excitation is far away from the eigenpulsations and the situation when the pulsation of the excitation is closed to one eigenpulsation, highlighting the beat phenomenon.

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