Frenkel, M.; Shoval, S.; Bormashenko, E. The Continuous Measure of Symmetry as a Dynamic Variable: A New Glance at the Three-Body Problem. Symmetry2023, 15, 2153.
Frenkel, M.; Shoval, S.; Bormashenko, E. The Continuous Measure of Symmetry as a Dynamic Variable: A New Glance at the Three-Body Problem. Symmetry 2023, 15, 2153.
Frenkel, M.; Shoval, S.; Bormashenko, E. The Continuous Measure of Symmetry as a Dynamic Variable: A New Glance at the Three-Body Problem. Symmetry2023, 15, 2153.
Frenkel, M.; Shoval, S.; Bormashenko, E. The Continuous Measure of Symmetry as a Dynamic Variable: A New Glance at the Three-Body Problem. Symmetry 2023, 15, 2153.
Abstract
The time evolution of the continuous measure symmetry for the system built of the three bodies interacting via the potential U(r)~1/r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of the pure gravitational interaction the three-body-system deviated from its initial symmetrical location, described by the Lagrange equilateral triangle, comes to collapse, accompanied by the growth of the continuous measure of symmetry. When three point bodies interact via the Coulomb repulsive interaction, the time evolution of CMS is quite different. CMS calculated for all of studied initial configurations of the point charges and all of their charge-to-mass ratios always comes to its asymptotic value with time, evidencing the stabilization of the shape of the triangle, constituted by the interacting bodies.
Keywords
three-body problem; Lagrange triangle; continuous measure of symmetry; gravity; Coulomb interaction; asymptotic value
Subject
Physical Sciences, Mathematical Physics
Copyright:
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