Some properties of the solution of the first-order variational equations of the restricted three-body problem

1967 ◽  
Vol 72 ◽  
pp. 865 ◽  
Author(s):  
John D. Hadjidemetriou
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Variational Equations ◽  
First Order ◽  
Three Body

scholarly journals Study of the stability of the perturbed solutions of the restricted three body problem

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 18-22
Author(s):  
MAA Khan ◽  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Variational Equations ◽  
First Order ◽  
Characteristic Exponents ◽  
Method Of Determination ◽  
The Stability ◽  
Three Body

In this paper we have been examined the stability of the perturbed solutions of the restricted three body problem. We have been restricted ourselves only to the first order variational equations. Our variational equations depend on the periodic solutions. Here the applications of the method of Fuchs and Floquet Proves to be complicated and hence we have been preferred Poincare's Method of determination of the characteristic exponents. With the determination of the characteristic exponents we have been abled to conclude regarding the stability of the generating solution. We have obtained that the motions are unstable in all the cases. By Poincare's implicit function theorem we have concluded that the stability would remain the same for small value of the parameter m and in all types of motion of the restricted three-body problem.BIBECHANA 13 (2016) 18-22 

Networks of periodic orbits in the circular restricted three-body problem with first order post-Newtonian terms

Meccanica ◽  
2019 ◽  
Vol 54 (15) ◽  
pp. 2339-2365 ◽  
Author(s):  
Euaggelos E. Zotos ◽  
K. E. Papadakis ◽  
Md Sanam Suraj ◽  
Amit Mittal ◽  
Rajiv Aggarwal
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
First Order ◽  
Three Body

scholarly journals Periodic Solution of the restricted three body problem

BIBECHANA ◽  
2013 ◽  
Vol 10 ◽  
pp. 44-51
Author(s):  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Periodic Solution ◽  
Analytic Continuation ◽  
Centrifugal Force ◽  
Periodic Motion ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
First Order ◽  
Three Body

The effect of perturbation in centrifugal force on the periodic solution of the restricted three-body problem representing analytic continuation of Keplerian rectilinear periodic motion has been examined. However, we have taken the perturbation in the centrifugal force to be of the order of μ, the reduced mass of the smaller primary. We have calculated the first order perturbations also. BIBECHANA 10 (2014) 44-51 DOI: http://dx.doi.org/10.3126/bibechana.v10i0.9310

scholarly journals Variational Chaos Indicators: Application to the Restricted Three-Body Problem

2014 ◽  
Vol 9 (S310) ◽  
pp. 35-38 ◽  
Author(s):  
Alexey M. Koksin ◽  
Vladimir A. Shefer
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Variational Equations ◽  
Three Body

AbstractA comparison of several known dynamical indicators of chaos based on the numerical integration of differential variational equations is performed. The comparison is implemented on the examples of studying dynamics in the planar circular restricted three-body problem.

scholarly journals Normalisation of Hamiltonian in photogravitational elliptic restricted three body problem with Poynting-Robertson drag

2015 ◽  
Vol 3 (1) ◽  
pp. 42
Author(s):  
Vivek Mishra ◽  
Bhola Ishwar
Keyword(s):  
Normal Form ◽  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Lagrangian Function ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
First Order ◽  
Order Part ◽  
Three Body

<p>In this paper, we have performed first order normalization in the photogravitational elliptic restricted three body problem  with Poynting-Robertson drag. We suppose that bigger primary as radiating and smaller primary is an oblate spheroid. We have found the Lagrangian and the Hamiltonian of the problem. Then, we have expanded the Lagrangian function in power series of x and y, where (x, y) are the coordinates of the triangular equilibrium points. Using Whittaker (1965) method, we have found that the second order part H<sub>2</sub> of the Hamiltonian is transformed into the normal form.</p>

On the modified circular restricted three-body problem with variable mass

New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body
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