First integrals for the equations of motion for test particles with internal structure

1991 ◽  
Vol 32 (9) ◽  
pp. 2473-2477 ◽  
Author(s):  
H. Fuchs
Keyword(s):  
Internal Structure ◽  
Equations Of Motion ◽  
First Integrals ◽  
Test Particles

scholarly journals The Quadrantid Meteor Stream: Past, Present and Future

1980 ◽  
Vol 90 ◽  
pp. 153-156
Author(s):  
David W. Hughes ◽  
Iwan P. Williams ◽  
Carl D. Murray
Keyword(s):  
Solar System ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Meteor Stream ◽  
Eccentric Anomaly ◽  
Test Particles ◽  
The Future ◽  
Runge Kutta

At the present time the orbit of the Quadrantid meteor stream not only intersects the orbit of Earth but also passes very close to the orbit of the planet Jupiter. This causes considerable perturbations. In a series of three papers (1,2,3) the authors replaced the myriad of meteoroids in the stream by ten test particles set at equal intervals of eccentric anomaly around the orbit. The equations of motion of these particles in the solar system were solved using a standard fourth order Runge–Kutta technique with self–adjusting step lengths. The orbits of the test particles were output at ten year intervals going back from the present to the year 300 B.C. and forward into the future to the year A.D. 3780.

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.

Noether gauge symmetries of geodesic motion in stationary and nonstatic Gödel-type spacetimes

2015 ◽  
Vol 38 ◽  
pp. 1560072 ◽  
Author(s):  
Ugur Camci
Keyword(s):  
Equations Of Motion ◽  
Complete Characterization ◽  
First Integrals ◽  
Geodesic Motion ◽  
Geodesic Equations ◽  
Gauge Symmetries ◽  
Geodesic Equations Of Motion

In this study, we obtain Noether gauge symmetries of geodesic motion for geodesic Lagrangian of stationary and nonstatic Gödel-type spacetimes, and find the first integrals of corresponding spacetimes to derive a complete characterization of the geodesic motion. Using the obtained expressions for [Formula: see text] of each spacetimes, we explicitly integrate the geodesic equations of motion for the corresponding stationary and nonstatic Gödel-type spacetimes.

scholarly journals Non-geodesic orbital and epicyclic frequencies in vicinity of slowly rotating magnetized neutron stars

2012 ◽  
Vol 8 (S290) ◽  
pp. 185-186
Author(s):  
Pavel Bakala ◽  
Martin Urbanec ◽  
Eva Šrámková ◽  
Zdeněk Stuchlík ◽  
Gabriel Török
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Equations Of Motion ◽  
Solution Of Equations ◽  
Test Particles ◽  
Perturbative Method ◽  
Relativistic Approach ◽  
Charged Test ◽  
The Magnetic Field

AbstractWe study non-geodesic corrections to the quasicircular motion of charged test particles in the field of magnetized slowly rotating neutron stars. The gravitational field is approximated by the Lense-Thirring geometry, the magnetic field is of the standard dipole character. Using a fully-relativistic approach we determine influence of the electromagnetic interaction (both attractive and repulsive) on the quasicircular motion. We focus on the behaviour of the orbital and epicyclic frequencies of the motion. Components of the four-velocity of the orbiting charged test particles are obtained by numerical solution of equations of motion, the epicyclic frequencies are obtained by using the standard perturbative method. The role of the combined effect of the neutron star magnetic field and its rotation in the character of the orbital and epicyclic frequencies is discussed.

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