Equations of motion for a variable-mass inertially-guided system.

1967 ◽  
Vol 4 (10) ◽  
pp. 1366-1368 ◽  
Author(s):  
ALAN M. SCHNEIDER
Keyword(s):  
Equations Of Motion ◽  
Variable Mass

Variable mass motion in the Hénon–Heiles system

2021 ◽  
pp. 2150150
Author(s):  
Abdullah A. Ansari ◽  
Elbaz I. Abouelmagd
Keyword(s):  
Test Particle ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Stationary Points ◽  
Mass Motion ◽  
Jacobi Integral

In this work, we analyze the motion properties of the test particle, that has a variable mass within the frame of Hénon–Heiles system. We derive the equations of motion of the test particle which varies its mass according to Jean’s law. We also determine the quasi-Jacobi integral which shows the effective variation due to variable mass parameters. Further, we studied the locations of stationary points and their stability, after using Meshcherskii spacetime inverse transformations.

scholarly journals Transient Annular Structures in Exploding Galaxies

1972 ◽  
Vol 44 ◽  
pp. 313-313
Author(s):  
J. L. Sěrsic
Keyword(s):  
Gravitational Field ◽  
Test Particle ◽  
Relative Velocity ◽  
Symmetry Axis ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Physical Space ◽  
Space Time ◽  
High Mass ◽  
New Variables

The explosive events going on in the central parts of some galaxies are related to a very high mass concentration. As an explosion is actually a drastic rearrangement of the concerned masses with energy release, the binding energy of the central core will change and, correspondingly, its effective gravitational mass. A test particle far from the nuclear region, although within the galaxy, will be moving accordingly in a variable-mass Newtonian gravitational field.On the other hand the observations suggest that explosions in galaxies have axial symmetry, so we are concerned with the global properties of the motion of a particle in a variable mass axisymmetric gravitational field. In order to get rid of the mass variation a space-time conformal transformation is made, which, after imposing some not very restrictive conditions, leads to a conservative potential in the new variables. This new potential has additional terms due to the elimination of the variable mass. The equations of motion in the new variables provide the motion of the test particle relative to an expanding or contracting background which depends on the choice of the transformation and the law of the mass variability. The problem is, at this point, formally similar to Hill's. It is possible to write an equation for the relative energy (a generalization of Jacobi's integral) and also to define surfaces of zero relative velocity for the infinitesimal particle. The general topological properties of these surfaces require singular points along the symmetry axis (analogous to the collinear Eulerian points) and also a dense set in a circumference on a plane perpendicular to the symmetry axis (analogous to the Lagrangian points). The latter one is the main feature characterizing the topology of the zero relative velocity surfaces. Even when we lift some of the restrictive conditions, the Lagrangian ring preserves its properties, as for example, the one of being the only region where zero-velocity curves and equi-potentials coincide when the configuration evolves in time (in the transformed space-time).It is easy to understand that the topology of the surfaces is kept when we reverse the transformation and go back to physical space-time. If the dust, gas or stars in the system has definite upper limits for its Jacobian constants, spatial segregation of them will arise, as is the case in radio-galaxies such as NGC 5128, NGC 1316, etc. where ringlike dust structures are observed.

Extended Kane’s Equations for Nonholonomic Variable Mass System

1982 ◽  
Vol 49 (2) ◽  
pp. 429-431 ◽  
Author(s):  
Z.-M. Ge ◽  
Y.-H. Cheng
Keyword(s):  
Equations Of Motion ◽  
Variable Mass ◽  
Mass System ◽  
Variable Mass System ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Variable Mass Systems

An extension of Kane’s equations of motion for nonholonomic variable mass systems is presented. As an illustrative example, equations of motion are formulated for a rocket car.

scholarly journals On algebraic integrals of equations of motion of a complex mechanical system

2021 ◽  
pp. 29-36
Author(s):  
Nikolay Makeyev ◽  
Keyword(s):  
Mechanical System ◽  
Gravity Field ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Equation Of Motion ◽  
First Integrals ◽  
Mass Composition ◽  
Complex Mechanical System ◽  
Fixed Pole ◽  
Variable Configuration

Criteria for the existence of certain types of algebraic first integrals of the equation of motion of a mechanical system of variable mass composition and variable configuration are given. The carrier body of the system (base body) rotates around a fixed pole in a stationary homogeneous gravity field under the influence of specified nonstationary forces. The types of partial integrals are indicated and restrictions are established that determine their existence.

scholarly journals Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem

2017 ◽  
Vol 2 (2) ◽  
pp. 529-542 ◽  
Author(s):  
Abdullah A. Ansari
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Solar Radiation Pressure ◽  
Basins Of Attraction ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractThe present paper investigates the motion of the variable infinitesimal body in circular restricted four variable bodies problem. We have constructed the equations of motion of the infinitesimal variable mass under the effect of source of radiation pressure due to which albedo effects are produced by another two primaries and one primary is considered as an oblate body which is placed at the triangular equilibrium point of the classical restricted three-body problem and also the variation of Jacobi Integral constant has been determined. We have studied numerically the equilibrium points, Poincaré surface of sections and basins of attraction in five cases (i. Third primary is placed at one of the triangular equilibrium points of the classical restricted three-body problem, ii. Variation of masses, iii. Solar radiation pressure, iv. Albedo effect, v. Oblateness effect.) by using Mathematica software. Finally, we have examined the stability of the equilibrium points and found that all the equilibrium points are unstable.

Equations of motion of the restricted problem of three bodies with variable mass

1983 ◽  
Vol 30 (3) ◽  
pp. 323-328 ◽  
Author(s):  
A. K. Shrivastava ◽  
Bhola Ishwar
Keyword(s):  
Restricted Problem ◽  
Equations Of Motion ◽  
Variable Mass
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