scholarly journals Matched Asymptotic Expansions to the Circular Sitnikov Problem with Long Period

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Marco Rosales-Vera
Keyword(s):  
Analytical Solutions ◽  
Asymptotic Expansions ◽  
Matched Asymptotic Expansions ◽  
Sitnikov Problem ◽  
Third Body ◽  
The Third ◽  
Long Period ◽  
Large Oscillation ◽  
Analytical Expressions

The circular Sitnikov problem is revisited, using matched asymptotic expansions. In the case of large oscillation periods, approximate analytical expressions for the period and the orbit of the third body are found. The results are compared with those described in the literature and show that the movement of the third body can be well described by two analytical solutions, the inner and outer solutions.

scholarly journals Modelling an isolated dust grain in a plasma using matched asymptotic expansions

2007 ◽  
Vol 73 (5) ◽  
pp. 793-810 ◽  
Author(s):  
N. ARINAMINPATHY ◽  
J. E. ALLEN ◽  
J. R. OCKENDON
Keyword(s):  
Asymptotic Expansions ◽  
Dusty Plasmas ◽  
Matched Asymptotic Expansions ◽  
Number Density ◽  
Plasma Parameters ◽  
Stationary Plasma ◽  
Dust Grain ◽  
Analytical Expressions ◽  
Single Set ◽  
Dust Plasma

AbstractThe study of dusty plasmas is of significant practical use and scientific interest. A characteristic feature of dust grains in a plasma is that they are typically smaller than the electron Debye distance, a property which we exploit using the technique of matched asymptotic expansions. We first consider the case of a spherical dust particle in a stationary plasma, employing the Allen–Boyd–Reynolds theory, which assumes cold, collisionless ions. We derive analytical expressions for the electric potential, the ion number density and ion velocity. This requires only one computation that is not specific to a single set of dust–plasma parameters, and sheds new light on the shielding distance of a dust grain. The extension of this calculation to the case of uniform ion streaming past the dust grain, a scenario of interest in many dusty plasmas, is less straightforward. For streaming below a certain threshold we again establish asymptotic solutions but above the streaming threshold there appears to be a fundamental change in the behaviour of the system.

The meniscus on the outside of a small circular cylinder

1974 ◽  
Vol 63 (4) ◽  
pp. 657-664 ◽  
Author(s):  
David F. James
Keyword(s):  
Differential Equation ◽  
Circular Cylinder ◽  
Asymptotic Expansions ◽  
Numerical Data ◽  
Matched Asymptotic Expansions ◽  
Term Result ◽  
Meniscus Height ◽  
Cylinder Radius ◽  
The Third

The method of matched asymptotic expansions is used to solve the differential equation describing the shape of a meniscus on the outside of a circular cylinder. Since the perturbation quantity is proportional to the cylinder radius, the solution is valid basically for small oylinders. The predicted meniscus height is compared with numerical data to determine the accuracy of the two-term result; the third term is found but does not improve the estimate.

On the use of the method of matched asymptotic expansions in propeller aerodynamics and acoustics

1992 ◽  
Vol 242 ◽  
pp. 117-143 ◽  
Author(s):  
H. H. Brouwer
Keyword(s):  
Asymptotic Expansions ◽  
Axial Flow ◽  
Matched Asymptotic Expansions ◽  
Analysis Method ◽  
Numerical Application ◽  
Outer Expansion ◽  
Line Equation ◽  
Practical Analysis ◽  
Lifting Line ◽  
Analytical Expressions

The applicability of the method of matched asymptotic expansions to both propeller aerodynamics and acoustics is investigated. The method is applied to a propeller with blades of high aspect ratio, in a uniform axial flow. The first two terms of the inner expansion and the first three terms of the outer expansion are considered. The matching yields an expression for the spanwise distribution of the downwash velocity. A numerical application shows that the first two terms of the inner solution do not yield an acceptable approximation for the downwash velocity. However, recasting the analytical expressions into an integral equation, similar to Prandtl's lifting line equation for wings, yields results for both aerodynamic and acoustic quantities, which agree well with experimental results. The method thus constitutes a practical analysis method for conventional propellers.

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

The Effect of the Third Body on the Fretting Wear Behavior of Coatings

2002 ◽  
Vol 11 (3) ◽  
pp. 288-293 ◽  
Author(s):  
Gui-Zhen Xu ◽  
Jia-Jun Liu ◽  
Zhong-Rong Zhou
Keyword(s):  
Wear Behavior ◽  
Fretting Wear ◽  
Third Body ◽  
The Third
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