scholarly journals Collision–Ejection Manifold and Collective Analytic Continuation of Simultaneous Binary Collisions in the PlanarN-Body Problem

1996 ◽  
Vol 203 (1) ◽  
pp. 55-77 ◽  
Author(s):  
Mohamed Sami ElBialy
Keyword(s):  
Analytic Continuation ◽  
Body Problem ◽  
Binary Collisions

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 An Adaptive Analytic Continuation Method for Computing the Perturbed Two-Body Problem State Transition Matrix

2020 ◽  
Vol 67 (4) ◽  
pp. 1412-1444 ◽  
Author(s):  
Tahsinul Haque Tasif ◽  
Tarek A. Elgohary
Keyword(s):  
Analytic Continuation ◽  
Taylor Series ◽  
Transition Matrix ◽  
Body Problem ◽  
State Transition ◽  
Higher Order ◽  
State Transition Matrix ◽  
Leibniz Rule ◽  
Double Precision ◽  
Two Body Problem

AbstractIn this work, the Taylor series based technique, Analytic Continuation is implemented to develop a method for the computation of the gravity and drag perturbed State Transition Matrix (STM) incorporating adaptive time steps and expansion order. Analytic Continuation has been developed for the two-body problem based on two scalar variables f and gp and their higher order time derivatives using Leibniz rule. The method has been proven to be very precise and efficient in trajectory propagation. The method is expanded to include the computation of the STM for the perturbed two-body problem. Leibniz product rule is used to compute the partials for the recursive formulas and an arbitrary order Taylor series is used to compute the STM. Four types of orbits, LEO, MEO, GTO and HEO, are presented and the simulations are run for 10 orbit periods. The accuracy of the STM is evaluated via RMS error for the unperturbed cases, symplectic check for the gravity perturbed cases and error propagation for the gravity and drag perturbed orbits. The results are compared against analytical and high order numerical solvers (ODE45, ODE113 and ODE87) in terms of accuracy. The results show that the method maintains double-precision accuracy for all test cases and 1-2 orders of magnitude improvement in linear prediction results compared to ODE87. The present approach is simple, adaptive and can readily be expanded to compute the full spherical harmonics gravity perturbations as well as the higher order state transition tensors.

scholarly journals Periodic Orbits of the First Kind in the Restricted Three-Body Problem When the More Massive Primary is an Oblate Spheroid

1978 ◽  
Vol 41 ◽  
pp. 355-355
Author(s):  
R.K. Sharma
Keyword(s):  
Analytic Continuation ◽  
Periodic Orbits ◽  
Equatorial Plane ◽  
Body Problem ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Canonical Variables ◽  
Three Body

AbstractThe existence of periodic orbits of the first kind using Delaunay’s canonical variables is established through analytic continuation in the planar restricted three-body problem when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion.

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