Perturbation Function

Perturbation Function

 

an auxiliary function in the theory of perturbations of celestial bodies. It depends on the coordinates of the given perturbed celestial body and on the coordinates and masses of the bodies attracting that body. The partial derivatives of the perturbation function with respect to the coordinates of the perturbed body are equal to the components of the acceleration imparted to the body in its relative motion about a central body as a result of the attraction of other celestial bodies. The concept of perturbation function was first introduced in 1776 by J. L. C. de Lagrange. In the series integration of the differential equations of the perturbed motion of celestial bodies, important problems are the expansion of the perturbation function in series, the investigation of the series’ convergence, and the estimation of the remainder terms.

References in periodicals archive ?
where the perturbation function [empty set](x) is evaluated by the following formulation, provided that in most epoxy/carbon materials, 4q> [p.sup.2]:
And perturbation function C(x), similar to Hashin's, is defined for most composites as
Once the perturbation function is obtained it is used to calculate stiffness reduction in the cracked laminate.
The power spectra density function, [PHI]([k.sub.x], [k.sub.z]), of the spatial random perturbation function, [[epsilon].sub.f](x, z), was calculated from (4) and is defined as
We obtained the spatial perturbation function of the random medium, [[epsilon].sub.f](x, z), by using the inverse Fourier transform of the random power spectra function.
In this paper, an Extended Inverse Chirp-Z Transform (EICZT) approach is proposed with a preprocessing operation in the azimuth-Doppler and range-time (Doppler-time) domain to compensate the range variance of the second order range terms, by using a perturbation function consisting of second-order and third-order range time variables.
A Perturbation Function Multiplication (PFM) is carried out in the Doppler-time domain to remove the range-variance of second order range terms, with a perturbation function consisting of second-order and third-order range time variables which is expressed as
The proposed EICZT approach conquered the limitation of conventional ICZT by introducing a perturbation function to deal with the range-variance of second-order range terms, which is essential in high squint cases.
By observing (22), (28), and (29), it turns out that we need to express K by [PSI] in order to express all perturbation functions [H.sub.0] (r), [H.sub.1] (r), [H.sub.2] (r), and K(r) in terms of [PSI].