Investigation resonance oscillation in the Sitnikov problem with optical emission

Mathematics. Physics. Mechanics


Kalas V. O.



Two equal masses move on two coplanar elliptic orbits around their barycentre while a third infinitely small mass bodymoves throw the mass center on a line perpendicularly to the motion plane ofthe first two masses. In the neighborhood of the stable equilibrium point is researchedone-dimensional oscillation of infinitely small mass body. Parametricresonance conditionwas defined. By theaveraging methodwe got averaged equations and investigated resonance and near-resonance region. Phase portrait was plotted. Example of this problem is a system of two stars with equal masses and emission. Between them areclouds of particles, which are subjected to gravitation and light pressure


Sitnikov problem; equilibrium; stability; parametric resonance; near-resonance region; phase portrait; bifurcation; averaging method; one-dimensional oscillation

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