IJPAM: Volume 115, No. 2 (2017)

Title

BIFURCATION ANALYSIS OF STABILITY OF
TRIANGULAR EQUILIBRIUM POINTS IN THE ELLIPTIC
RESTRICTED PROBLEM OF THREE BODIES

Authors

T. Usha$^1$, A. Narayan$^2$
$^{1,2}$Bhilai Institute of Technology
Durg, INDIA

Abstract

This paper analyses the local bifurcation of linear stability of motion near the triangular equilibrium points in the neighborhood of parametric resonance frequency $\omega_2=\frac{1}{2}$. The periodic linear Hamiltonian system considered is dependent on small parameter v(true anamoly). The system experiences the resonance at $\omega_2=\frac{1}{2}$ for circular and elliptic orbits, respectively. The Hamiltonian is made independent of time using canonical transformations. It is found that the values of mass ratio, $\mu$ are less than the critical value $\mu_c$ in resonant case, for both orbits. The boundary of the stability region are found in form of equations for both orbits, circular and elliptic (for small values of e). The regions of stability and instability are plotted in the graphs. There is a shift in the bifurcation points of mass ratio,$\mu$ from the critical value $\mu_c$ as a result of increase in values of radiation pressure($\delta$), triaxiality parameters($\sigma_1$ and $\sigma_2$).

History

Received: December 29, 2016
Revised: April 7, 2017
Published: July 14, 2017

AMS Classification, Key Words

AMS Subject Classification: 70F15
Key Words and Phrases: celestial mechanics, elliptical restricted three body problem, Lagrangian points, stability, oblateness, parametric resonance, bifurcation, local bifurcation

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How to Cite?

DOI: 10.12732/ijpam.v115i2.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 2
Pages: 271 - 284


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