On a global expansion of the disturbing function in the planar elliptic restricted three-body problem

1996 ◽  
Vol 64 (4) ◽  
pp. 313-350 ◽  
Author(s):  
C. Beaug�
Keyword(s):  
Body Problem ◽  
Disturbing Function ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Global Expansion ◽  
Three Body

Special cases of the restricted problem of three bodies

1966 ◽  
Vol 25 ◽  
pp. 187-193 ◽  
Author(s):  
J. Schubart
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Disturbing Function ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Long Period ◽  
Period Effects ◽  
Special Cases ◽  
Three Body

The long-period effects in nearly commensurable cases of the restricted three-body problem were studied according to the ideas of Poincaré. The secular and critical terms of the disturbing function were isolated by a numerical averaging process, by use of an IBM 7094 computer.

scholarly journals High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-23 ◽  
Author(s):  
Takashi Ito
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Semimajor Axis ◽  
High Order ◽  
Numerical Quadrature ◽  
Disturbing Function ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Axis Ratio ◽  
Three Body

Terms in the analytic expansion of the doubly averaged disturbing function for the circular restricted three-body problem using the Legendre polynomial are explicitly calculated up to the fourteenth order of semimajor axis ratio (α) between perturbed and perturbing bodies in the inner case (α<1), and up to the fifteenth order in the outer case (α>1). The expansion outcome is compared with results from numerical quadrature on an equipotential surface. Comparison with direct numerical integration of equations of motion is also presented. Overall, the high-order analytic expansion of the doubly averaged disturbing function yields a result that agrees well with the numerical quadrature and with the numerical integration. Local extremums of the doubly averaged disturbing function are quantitatively reproduced by the high-order analytic expansion even when α is large. Although the analytic expansion is not applicable in some circumstances such as when orbits of perturbed and perturbing bodies cross or when strong mean motion resonance is at work, our expansion result will be useful for analytically understanding the long-term dynamical behavior of perturbed bodies in circular restricted three-body systems.

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

scholarly journals GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

2007 ◽  
Vol 17 (04) ◽  
pp. 1151-1169 ◽  
Author(s):  
MARIAN GIDEA ◽  
JOSEP J. MASDEMONT
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Libration Point ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lyapunov Orbits ◽  
Homoclinic Connections ◽  
Three Body

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

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