Lagrange's Theorem on the Center of Mass of a System of Particles

1972 ◽  
Vol 40 (1) ◽  
pp. 205-207 ◽  
Author(s):  
Millard F. Beatty
Keyword(s):  
Center Of Mass ◽  
System Of Particles ◽  
Lagrange's Theorem

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Center-of-mass variables in the relativistic Lagrangian dynamics of a system of particles

1994 ◽  
Vol 101 (3) ◽  
pp. 1443-1453 ◽  
Author(s):  
R. P. Gaida ◽  
V. I. Tretyak ◽  
Yu. G. Yaremko
Keyword(s):  
Center Of Mass ◽  
Lagrangian Dynamics ◽  
System Of Particles

scholarly journals Hyperbolic Center of Mass for a System of Particles on the Poincare Upper Half-Plane

2019 ◽  
Vol 14 (2) ◽  
pp. 49-53
Author(s):  
P. Ortega Palencia ◽  
Ruben Dario Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Half Plane ◽  
Center Of Mass ◽  
System Of Particles ◽  
Upper Half Plane

The Center of Mass Influences Normal Attentional Orienting

1994 ◽  
Author(s):  
Marcia Grabowecky ◽  
Lynn C. Robertson ◽  
Anne Treisman
Keyword(s):  
Center Of Mass ◽  
Attentional Orienting

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

Exploring Baryon Rich Matter with Heavy-Ion Collisions

2019 ◽  
Vol 64 (7) ◽  
pp. 583 ◽  
Author(s):  
S. Harabasz
Keyword(s):  
Center Of Mass ◽  
Heavy Ion ◽  
State Density ◽  
Heavy Nuclei ◽  
First Order ◽  
Center Of Mass Energy ◽  
Ion Collisions ◽  
Deconfinement Phase Transition ◽  
Ground State Density

Collisions of heavy nuclei at (ultra-)relativistic energies provide a fascinating opportunity to re-create various forms of matter in the laboratory. For a short extent of time (10-22 s), matter under extreme conditions of temperature and density can exist. In dedicated experiments, one explores the microscopic structure of strongly interacting matter and its phase diagram. In heavy-ion reactions at SIS18 collision energies, matter is substantially compressed (2–3 times ground-state density), while moderate temperatures are reached (T < 70 MeV). The conditions closely resemble those that prevail, e.g., in neutron star mergers. Matter under such conditions is currently being studied at the High Acceptance DiElecton Spectrometer (HADES). Important topics of the research program are the mechanisms of strangeness production, the emissivity of matter, and the role of baryonic resonances herein. In this contribution, we will focus on the important experimental results obtained by HADES in Au+Au collisions at 2.4 GeV center-of-mass energy. We will also present perspectives for future experiments with HADES and CBM at SIS100, where higher beam energies and intensities will allow for the studies of the first-order deconfinement phase transition and its critical endpoint.

Effects of Stiffness and the Variation of Center of Mass on Rocket Motion

2020 ◽  
Vol 13 (1) ◽  
pp. 16
Author(s):  
Dam Viet Phuong ◽  
Quoc Tru Vu ◽  
Anh Tuan Nguyen
Keyword(s):  
Center Of Mass
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