Object

Title: The Three-body Problem in Riemannian Geometry. Hidden Irreversibility of the Classical Dynamical System

Abstract:

The classical three-body problem is formulated as a problem of geodesic flows on a Riemannian manifold. It is proved that a curved space allows to detect new hidden symmetries of the internal motion of a dynamical system and reduces the three-body problem to the system of 6th order. It is shown that the equivalence of the original Newtonian three-body problem and the developed representation provides coordinate transformations together with an underdetermined system of algebraic equations. The latter makes the system of geodesic equations relative to the evolution parameter (internal time), i.e. to the arc length of the geodesic curve, irreversible.

Publisher:

Springer

Date of publication:

03.10.2019

Identifier:

oai:noad.sci.am:136192

DOI:

10.1134/S1995080219080080

Language:

English

Journal or Publication Title:

Lobachevskii Journal of Mathematics

Volume:

40

Number:

8

URL:

click here to follow the link

Affiliation:

Institute for Informatics and Automation Problems of NAS RA

Object collections:

Last modified:

May 3, 2021

In our library since:

Apr 20, 2021

Number of object content hits:

8

All available object's versions:

https://noad.sci.am/publication/149757

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