scholarly journals Extended two-body problem for rotating rigid bodies

2021 ◽  
Vol 133 (8) ◽  
Author(s):  
Alex Ho ◽  
Margrethe Wold ◽  
John T. Conway ◽  
Mohammad Poursina
Keyword(s):  
Degrees Of Freedom ◽  
Body Problem ◽  
Major Axis ◽  
Rigid Bodies ◽  
Semi Major Axis ◽  
Simulation Accuracy ◽  
Two Body Problem ◽  
Tumbling Motion ◽  
A New Technique ◽  
Test Scenarios

AbstractA new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for pairs of spheroids and ellipsoids with 12 degrees of freedom. We demonstrate the method with two dimensionless test scenarios, one where tumbling motion develops, and one where the motion of the bodies resemble spinning tops. We also test the method on the asteroid binary (66391) 1999 KW4, where both components are modelled either as spheroids or ellipsoids. The two different shape models have negligible effects on the eccentricity and semi-major axis, but have a larger impact on the angular velocity along the z-direction. In all cases, energy and total angular momentum is conserved, and the simulation accuracy is kept at the machine accuracy level.

scholarly journals Krein Stability in the Disturbed Two-Body Problem

1992 ◽  
Vol 152 ◽  
pp. 369-374
Author(s):  
R. R. Cordeiro ◽  
R. Vieira Martins
Keyword(s):  
Small Parameter ◽  
Integrable Systems ◽  
Body Problem ◽  
Major Axis ◽  
Semi Major Axis ◽  
First Order ◽  
Two Body Problem

We present a method for the study of the Krein signature in perturbed Hamiltonian integrable systems. The method is developed up to first order in the small parameter. We apply this method to a particular instance of the two-body problem in which the semi-major axis is not affected by the perturbation.

Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation

2004 ◽  
Author(s):  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Matrix ◽  
Explicit Time Integration ◽  
Penalty Formulation ◽  
A New Technique ◽  
Rigid Multibody

A new technique for modeling rigid bodies undergoing spatial motion using an explicit time-integration finite element code is presented. The key elements of the technique are: (a) use of the total rotation matrix relative to the inertial frame to measure the rotation of the rigid bodies; (b) time-integration of the rotational equations of motion in a body fixed (material) frame, with the resulting incremental rotations added to the total rotation matrix; (c) penalty formulation for creating connection points (virtual nodes which do not add extra degrees of freedom) on the rigid-body where joints can be placed. The use of the rotation matrix along with incremental rotation updates circumvents the problem of singularities associated with other types of three and four parameter rotation measures. Benchmark rigid multibody dynamics problems are solved to demonstrate the accuracy of the present technique.

scholarly journals Investigation of the Stability of a Test Particle in the Vicinity of Collinear Points with the Additional Influence of an Oblate Primary and a Triaxial-Stellar Companion in the Frame of ER3BP

2018 ◽  
Vol 13 ◽  
pp. 12-27 ◽  
Author(s):  
Aminu Abubakar Hussain ◽  
Aishetu Umar ◽  
Jagadish Singh
Keyword(s):  
Numerical Analysis ◽  
Body Problem ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Primary Body ◽  
Additional Influence ◽  
The Stability ◽  
Three Body

We investigate in the elliptic framework of the restricted three-body problem, the motion around the collinear points of an infinitesimal particle in the vicinity of an oblate primary and a triaxial stellar companion. The locations of the collinear points are affected by the eccentricity of the orbits, oblateness of the primary body and the triaxiality and luminosity of the secondary. A numerical analysis of the effects of the parameters on the positions of collinear points of CEN X-4 and PSR J1903+0327 reveals a general shift away from the smaller primary with increase in eccentricity and triaxiality factors and a shift towards the smaller primary with increase in the semi-major axis and oblateness of the primary on L1. The collinear points remain unstable in spite of the introduction of these parameters.

scholarly journals The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at J4

2021 ◽  
Vol 17 ◽  
pp. 1-11
Author(s):  
Jagadish Singh ◽  
Tyokyaa K. Richard
Keyword(s):  
Binary Systems ◽  
Body Problem ◽  
Equilibrium Points ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Out Of Plane ◽  
Three Body ◽  
Plane Equilibrium

We have investigated the motion of the out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at J4 of the smaller primary in the field of stellar binary systems: Xi- Bootis and Sirius around their common center of mass in elliptic orbits. The positions and stability of the out-of-plane equilibrium points are greatly affected on the premise of the oblateness at J4 of the smaller primary, semi-major axis and the eccentricity of their orbits. The positions L6, 7 of the infinitesimal body lie in the xz-plane almost directly above and below the center of each oblate primary. Numerically, we have computed the positions and stability of L6, 7 for the aforementioned binary systems and found that their positions are affected by the oblateness of the primaries, the semi-major axis and eccentricity of their orbits. It is observed that, for each set of values, there exist at least one complex root with positive real part and hence in Lyapunov sense, the stability of the out-of-plane equilibrium points are unstable.

scholarly journals Effect on L4,5 in the ER3BP when Both Primaries are Radiating with Oblateness up to Zonal Harmonic J4

2019 ◽  
Vol 83 ◽  
pp. 1-11
Author(s):  
Jagadish Singh ◽  
Blessing Ashagwu
Keyword(s):  
Body Problem ◽  
Critical Mass ◽  
Major Axis ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Zonal Harmonic ◽  
Triangular Points ◽  
Oblate Spheroids ◽  
Three Body

This study examines the triangular points in the elliptic restricted three-body problem when both primaries are sources of radiation as well as oblate spheroids with oblateness up to zonal harmonic J4. The positions of triangular points and their critical mass ratio are seen to be affected by the eccentricity, semi major axis, radiation and oblateness of both primaries up to zonal harmonic J4. We highlight the effects of the said parameters on the locations of the triangular points of 61 CYGNI and STRUVE 2398. The triangular points of these systems are found to be unstable.

scholarly journals Effects of radiation and triaxiality of triangular equilibrium points in elliptical restricted three body problem

2015 ◽  
Vol 3 (2) ◽  
pp. 97 ◽  
Author(s):  
Ashutosh Narayan ◽  
Krishna Kumar Pandey ◽  
Sandip Kumar Shrivastava
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
The Stability ◽  
Three Body

<p>This paper studies effects of the triaxiality and radiation pressure of both the primaries on the stability of the infinitesimal motion about triangular equilibrium points in the elliptical restricted three body problem(ER3BP), assuming that the bigger and the smaller primaries are triaxial and the source of radiation as well. It is observed that the motion around these points is stable under certain condition with respect to the radiation pressure and oblate triaxiality. The critical mass ratio depends on the radiation pressure, triaxiality, semi -major axis and eccentricity of the orbits. It is further analyzed that an increase in any of these parameters has destabilizing effects on the orbits of the infinitesimal.</p>

scholarly journals The Qualitative Explanation of Observed Peculiarities of Hecuba and Hilda Asteroids Distribution by a Common Investigation

1992 ◽  
Vol 152 ◽  
pp. 139-144
Author(s):  
Elena V. Alfimova ◽  
Igor A. Gerasimov
Keyword(s):  
Body Problem ◽  
Gravitational Constant ◽  
Central Body ◽  
Major Axis ◽  
Mass Point ◽  
Three Body Problem ◽  
Qualitative Explanation ◽  
Semi Major Axis ◽  
Planar Case ◽  
Three Body

Let us consider the planar case of the circular restricted three-body problem. The mass of central body is unit, the radius of the circular orbit of perturbing point P′ (of mass μ = 1/1047.39 according to Jupiter's mass) is also unit and the other unit is such that the gravitational constant is equal to 1. The Keplerian elements of the perturbed mass point P (asteroid), with semi-major axis α < 1, are given by usual notations; the elements of P‘ are indicated with a prime (’).

Detection and Characterization of earth-like Planets

1997 ◽  
Vol 161 ◽  
pp. 299-311 ◽  
Author(s):  
Jean Marie Mariotti ◽  
Alain Léger ◽  
Bertrand Mennesson ◽  
Marc Ollivier
Keyword(s):  
Direct Detection ◽  
Contrast Ratio ◽  
Angular Size ◽  
Physical Nature ◽  
Major Axis ◽  
Infrared Emission ◽  
Space Technology ◽  
Semi Major Axis ◽  
Earth Like Planets ◽  
Visible Wavelengths

AbstractIndirect methods of detection of exo-planets (by radial velocity, astrometry, occultations,...) have revealed recently the first cases of exo-planets, and will in the near future expand our knowledge of these systems. They will provide statistical informations on the dynamical parameters: semi-major axis, eccentricities, inclinations,... But the physical nature of these planets will remain mostly unknown. Only for the larger ones (exo-Jupiters), an estimate of the mass will be accessible. To characterize in more details Earth-like exo-planets, direct detection (i.e., direct observation of photons from the planet) is required. This is a much more challenging observational program. The exo-planets are extremely faint with respect to their star: the contrast ratio is about 10−10at visible wavelengths. Also the angular size of the apparent orbit is small, typically 0.1 second of arc. While the first point calls for observations in the infrared (where the contrast goes up to 10−7) and with a coronograph, the latter implies using an interferometer. Several space projects combining these techniques have been recently proposed. They aim at surveying a few hundreds of nearby single solar-like stars in search for Earth-like planets, and at performing a low resolution spectroscopic analysis of their infrared emission in order to reveal the presence in the atmosphere of the planet of CO H2O and O3. The latter is a good tracer of the presence of oxygen which could be, like on our Earth, released by biological activity. Although extremely ambitious, these projects could be realized using space technology either already available or in development for others missions. They could be built and launched during the first decades on the next century.

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