On the photogravitational R4BP when the third primary is a triaxial rigid body

2016 ◽  
Vol 361 (12) ◽  
Author(s):  
Md Chand Asique ◽  
Umakant Prasad ◽  
M. R. Hassan ◽  
Md Sanam Suraj
Keyword(s):  
Rigid Body ◽  
The Third ◽  
Triaxial Rigid Body

scholarly journals Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

2017 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Rigid Body ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Triaxial Rigid Body ◽  
Three Body ◽  
Infinitesimal Mass

This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).

Mathematical aspects of molecular replacement. III. Properties of space groups preferred by proteins in the Protein Data Bank

2015 ◽  
Vol 71 (2) ◽  
pp. 186-194 ◽  
Author(s):  
G. Chirikjian ◽  
S. Sajjadi ◽  
D. Toptygin ◽  
Y. Yan
Keyword(s):  
Rigid Body ◽  
Protein Data Bank ◽  
Data Bank ◽  
Continuous Group ◽  
Molecular Replacement ◽  
Macromolecular Crystallography ◽  
Coset Space ◽  
Space Groups ◽  
The Third ◽  
Rigid Body Motions

The main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\Gwhere Γ is the Sohncke group of the macromolecular crystal andGis the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.

scholarly journals Periodic orbits in the restricted problem of three bodies in a three-dimensional coordinate system when the smaller primary is a triaxial rigid body

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Awadhesh Kumar Poddar ◽  
Divyanshi Sharma
Keyword(s):  
Perturbation Theory ◽  
Rigid Body ◽  
Coordinate System ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
General Perturbation ◽  
Triaxial Rigid Body ◽  
Three Dimensional Coordinate

AbstractIn this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when μ = 0. Finally, it establishes the canonical set (l, L, g, G, h, H) and forms the basic general perturbation theory for the problem.

Command shaping with reduced maneuvering time for crane control

2020 ◽  
pp. 107754632094087
Author(s):  
Emad Khorshid ◽  
Abdulaziz Al-Fadhli ◽  
Khalid Alghanim ◽  
Jasem Baroon
Keyword(s):  
Rigid Body ◽  
Quick Response ◽  
Command Shaping ◽  
System Parameters ◽  
Second Stage ◽  
The Third ◽  
Third Stage ◽  
Control Objective ◽  
Time Optimal ◽  
Three Stages

This study introduces a modified near-time–optimal rigid-body command that represents the fastest possible command profile based on using the full input capabilities of the system, considering rest-to-rest motion. The control objective is to have the shortest maneuvering time suitable for handling insensitive payloads. The rest-to-rest motion is divided into three stages. The first stage includes a quick response with maximum trolley acceleration. The second stage involves cruising at the maximum trolley velocity. The third stage provides deceleration, where both zero vibration and the zero vibration derivative are applied. The proposed shaper is simulated numerically for testing its performance. The theoretical findings were validated experimentally using a prototype crane. This study’s major finding demonstrates that the new technique succeeded in reducing the maneuvering time with zero vibration at the end of the motion. Moreover, the results show the insensitivity of the proposed shaper to variations in system parameters using a zero vibration derivative shaper.

Instantaneous Properties of Trajectories Generated by Planar, Spherical, and Spatial Rigid Body Motions

1982 ◽  
Vol 104 (1) ◽  
pp. 39-50 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
Motion Trajectories ◽  
The Third ◽  
Moving Body ◽  
Rigid Body Motions ◽  
Point Trajectories

This paper develops relationships between the instantaneous invariants of a motion and the local shape of the trajectories generated during the motion. We consider the point trajectories generated by planar and spherical motions and the line trajectories generated by spatial motion. Those points or lines which generate special trajectories are located on (and define) so-called boundary loci in the moving body. These boundary loci define regions, within the body, for which all the points or lines generate similarly shaped trajectories. The shapes of these boundaries depend directly upon the invariants of the motion. It is shown how to qualitatively determine the fundamental trajectory shapes, analyze the effect of the invariants on the boundary loci, and how to combine these results to visualize the motion trajectories to the third order.

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