On-Orbit Operational Range Computation Using Gauss’s Variational Equations with J2 Perturbations

2014 ◽  
Vol 37 (2) ◽  
pp. 608-622 ◽  
Author(s):  
Marcus J. Holzinger ◽  
Daniel J. Scheeres ◽  
R. Scott Erwin
Keyword(s):  
Variational Equations ◽  
Operational Range ◽  
Range Computation

On the motion of comet P/d’Arrest

1974 ◽  
Vol 22 ◽  
pp. 145-148
Author(s):  
W. J. Klepczynski
Keyword(s):  
Equations Of Motion ◽  
Variational Equations ◽  
Partial Derivatives

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM

2008 ◽  
Vol 17 (03) ◽  
pp. 285-297 ◽  
Author(s):  
ABDOSLLAM M. ABOBAKER ◽  
A. B. MOUBISSI ◽  
TH. B. EKOGO ◽  
K. NAKKEERAN
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Pulse Width ◽  
Schrodinger Equation ◽  
Pulse Propagation ◽  
Nonlinear Schrodinger Equation ◽  
Fiber System ◽  
Variational Equations ◽  
Nonlinear Schrödinger ◽  
The Given

We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

Performance evaluation of a non-linear error model for underwater range computation utilizing GPS sonobuoys

2010 ◽  
Vol 19 (7) ◽  
pp. 1057-1067 ◽  
Author(s):  
Ahmed El-Shafie ◽  
Abdalla Osman ◽  
Aboelmagd Noureldin ◽  
Aini Hussain
Keyword(s):  
Performance Evaluation ◽  
Error Model ◽  
Non Linear ◽  
Range Computation

Exponential Stability in Mean Square and Stochastic Variational Equations

2011 ◽  
Author(s):  
Adina Păucă ◽  
Diana Stoica ◽  
Ludovic Dan Lemle ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Mean Square ◽  
Variational Equations ◽  
Stability In Mean Square

scholarly journals Variational Equations of Schroedinger-Type in Non-cylindrical Domains

2001 ◽  
Vol 171 (1) ◽  
pp. 63-87 ◽  
Author(s):  
Marco Luigi Bernardi ◽  
Gianni Arrigo Pozzi ◽  
Giuseppe Savaré
Keyword(s):  
Variational Equations ◽  
Cylindrical Domains
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