scholarly journals Physics and Mechanizm of Creation, Separation and Orbiting of the Solar System Bodies Based on Jacobi Dynamics

2021 ◽  
Vol 4 (1) ◽  
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Continuous Media ◽  
System Of Equations ◽  
Many Body ◽  
Natural Systems ◽  
Solar System Bodies ◽  
The Many ◽  
Jacobi Dynamics

Our work sets forth and builds upon the fundamentals of the dynamics of natural systems in formulating the problem presented by Jacobi in his famous lecture series “Vorlesung über Dynamik”. In the dynamics of systems described by models of discrete and continuous media, the many-body problem is usually solved in some approximation, or the behavior of the medium is studied at each point of the space it occupies. Such an approach requires the system of equations of motion to be written in terms of space co-ordinates and velocities, in which case the requirements of an internal observer for a detailed description of the processes are satisfied.

scholarly journals On the conservation of momentum

1946 ◽  
Vol 186 (1007) ◽  
pp. 432-442
Keyword(s):  
Angular Momentum ◽  
Potential Energy ◽  
Body Problem ◽  
Equations Of Motion ◽  
Gravitational Theory ◽  
Gravitational Potential Energy ◽  
Many Body ◽  
Conservation Of Momentum ◽  
The Many ◽  
The Universe

1. Scope of the paper . The present paper is a continuation of an earlier sequence in these Proceedings , entitled ‘ The inverse square law of gravitation, I, II and III’ (Milne 1936, 1937c), which itself was connected with another sequence entitled ‘Kinematics, dynamics and the scale of time, I, II and III ’(Milne 1937 a,b ). In the latter sequence the relations between t -dynamics and r -dynamics were obtained. In the former sequence a formula for the gravitational potential energy of two particles was isolated which was Lorentz-invariant for transformations from any one fundamental observer in the expanding substratum to any other fundamental observer; and the corresponding equations of motion in t -measure were obtained. In the present paper I obtain relations which correspond to the integrals of linear and angular momentum in the many-body problem of classical gravitational theory. I conclude that Einstein’s form of the conservation of linear momentum in special relativity holds good in the universe at large only in the case of a collinear set of particles moving along their line of collinearity, and I give the modification of the law of conservation which should hold good in other cases.

A new method in the many-body problem: II

1996 ◽  
Vol 29 (1) ◽  
pp. 133-142
Author(s):  
I V Krasovsky ◽  
V I Peresada
Keyword(s):  
Body Problem ◽  
New Method ◽  
Many Body ◽  
The Many

An Algebraic Framework for the Many-Body Problem

1996 ◽  
pp. 357-399
Author(s):  
Werner O. Amrein ◽  
Anne Boutet Monvel ◽  
Vladimir Georgescu
Keyword(s):  
Body Problem ◽  
Many Body ◽  
Algebraic Framework ◽  
The Many

An Algebraic Framework for the Many-Body Problem

1996 ◽  
pp. 357-399
Author(s):  
Werner O. Amrein ◽  
Anne Boutet Monvel ◽  
Vladimir Georgescu
Keyword(s):  
Body Problem ◽  
Many Body ◽  
Algebraic Framework ◽  
The Many
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