THE LORF ORBIT EQUATION WITH FULL QUATERNIONS

In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.

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Nonlinear two-field models from orbit equation deformations

Physical Review D ◽

10.1103/physrevd.84.105001 ◽

2011 ◽

Vol 84 (10) ◽

Cited By ~ 4

Author(s):

A. de Souza Dutra ◽

P. E. D. Goulart

Keyword(s):

Orbit Equation

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AN EXPLICIT HIGH ORDER PREDICTOR-CORRECTOR METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202595000103 ◽

1995 ◽

Vol 05 (02) ◽

pp. 159-166 ◽

Cited By ~ 20

Author(s):

T.E. SIMOS

Keyword(s):

Initial Value Problems ◽

Interval Of Periodicity ◽

Phase Lag ◽

Initial Value ◽

Large Interval ◽

Type Method ◽

Algebraic Order ◽

Periodic Initial Value Problems ◽

Orbit Equation ◽

Predictor Corrector

An explicit Runge-Kutta type method is developed here. This method has an algebraic order six, a large interval of periodicity and a phase-lag of order eight. It is much more efficient than other well known methods when applying to an orbit equation.

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The 2nd-order Post-Newtonian Orbit Equation of Light

Chinese Astronomy and Astrophysics ◽

10.1016/j.chinastron.2008.10.006 ◽

2008 ◽

Vol 32 (4) ◽

pp. 423-428 ◽

Cited By ~ 1

Author(s):

Yu Xiao ◽

Bao-Jun Fei ◽

Wei-Jin Sun ◽

Cheng-Xiang Ji

Keyword(s):

Orbit Equation

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HIROTA BILINEAR FORM FOR THE SUPER-KdV HIERARCHY

Modern Physics Letters A ◽

10.1142/s0217732393001471 ◽

1993 ◽

Vol 08 (18) ◽

pp. 1739-1745 ◽

Cited By ~ 42

Author(s):

I.N. MCARTHUR ◽

C.M. YUNG

Keyword(s):

Lie Algebra ◽

Bilinear Form ◽

Infinite Dimensional ◽

Kdv Hierarchy ◽

Hirota Bilinear Form ◽

Group Orbit ◽

Orbit Equation ◽

Infinite Dimensional Lie Algebra ◽

Hirota Bilinear

The integrability of the super-KdV hierarchy suggests that it can be written in Hirota bilinear form as the group orbit equation for some infinite-dimensional Lie algebra. We show how the first few equations in the hierarchy can be written in Hirota bilinear form. We also conjecture a bilinear expression for the whole super-KdV hierarchy and check it to reasonably high orders. A by-product is an expression for the ordinary KdV hierarchy which provides an alternative to the ones obtained by Date et al. and Kac and Wakimoto.

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