The gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. J39-J42 ◽  
Author(s):  
Juan García-Abdeslem
Keyword(s):  
Rectangular Prism ◽  
Gravitational Attraction ◽  
Cubic Polynomial

THE GRAVITATIONAL ATTRACTION OF A RIGHT RECTANGULAR PRISM

Geophysics ◽  
1966 ◽  
Vol 31 (2) ◽  
pp. 362-371 ◽  
Author(s):  
Dezsö Nagy
Keyword(s):  
Gravity Field ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Vertical Component ◽  
Gravitational Effect ◽  
Rectangular Prism ◽  
Gravitational Attraction ◽  
Closed Expression ◽  
Building Element ◽  
Terrain Corrections

The derivation of a closed expression is presented to calculate the vertical component of the gravitational attraction of a right rectangular prism, with sides parallel to the coordinate axis. As any configuration can be expressed as the sum of prisms of various sizes and densities, the computation of the total gravitational effect of bodies of arbitrary shapes at any point outside of or on the boundary of the bodies is straightforward. To calculate the gravitational effect of the “unit” building element a subroutine called Prism has been developed, tested, and incorporated, in one program to calculate terrain corrections, and in another program for three‐dimensional analysis of a gravity field.

On: “THE GRAVITATIONAL ATTRACTION OF A RIGHT RECTANGULAR PRISM,” BY DEZSÖ NAGY (GEOPHYSICS, APRIL, 1966, PP. 362–371)

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 987-987 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Vertical Component ◽  
Rectangular Prism ◽  
Gravitational Attraction ◽  
Gravitational Effects ◽  
Rectangular Parallelopiped

You might be interested to note that the results obtained by Nagy (1966) and published in Geophysics concerning the vertical component of the gravitational attraction of a right rectangular prism not only had been published previously by Sorokin and Haáz but also were derived and published (in English) 136 years ago by Everest (1830, p. 94–97). Everest calculated closed expressions which are equivalent to that of Nagy for the horizontal and vertical gravitational effects of a rectangular parallelopiped and used these equations to estimate the topographic deflection of the plumb bob due to the Satpura Range in India.

On: “THE GRAVITATIONAL ATTRACTION OF A RIGHT RECTANGULAR PRISM,” BY DEZSÖ NAGY (GEOPHYSICS, APRIL, 1966, PP. 362–371)

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 987-987 ◽  
Author(s):  
J. Cl. De Bremaecker
Keyword(s):  
Rectangular Prism ◽  
Gravitational Attraction ◽  
Simple Method ◽  
Coordinate Axis

The recent paper by Dezsö Nagy, “The gravitational attraction of a right rectangular prism,” is certainly of great interest. It might be pointed out, however, that in his textbook published in 1930, MacMillan already gave a formula for computing the potential of this body, as well as an extremely simple method to compute the derivatives along a coordinate axis. The Dover reprint is widely available.

On: “The Gravitational Attraction of a Right Rectangular Prism” by Dezsö Nagy (GEOPHYSICS, April 1966, p. 362–371)

Geophysics ◽  
1967 ◽  
Vol 32 (5) ◽  
pp. 920-920
Author(s):  
P. Vallabh Sharma
Keyword(s):  
Closed Form ◽  
Rectangular Prism ◽  
Gravitational Attraction

I would like to offer the following comment on the paper “The Gravitational Attraction of a Right Rectangular Prism” by Nagy in the April 1966 issue of Geophysics. It might be of interest to note that besides the papers (Sorokin, 1951; Haáz, 1953) which have been cited by the author, an earlier publication by Ansel (1936) also gives a solution in closed form for the gravitational attraction of a rectangular prism. Furthermore, Müller (1963) has given a solution which is valid for all possible positions of the prism with vertical sides.

To: “The Gravitational Attraction of a Right Rectangular Prism” by Dezsö Nagy, April, 1966, p. 362–371

Geophysics ◽  
1967 ◽  
Vol 32 (2) ◽  
pp. 368-368
Keyword(s):  
Rectangular Prism ◽  
Gravitational Attraction ◽  
Research Scientist ◽  
Pan American

Some typographical errors in the paper entitled “The Gravitational Attraction of a Right Rectangular Prism” by Dezsö Nagy, April, 1966, p. 362–371, were kindly pointed out by Donald B. Johnson, Research Scientist, Pan American Corp., Tulsa.

Maclaurin on Occasionalism: A Reply to Ablondi

2016 ◽  
Vol 14 (1) ◽  
pp. 125-135
Author(s):  
Patrick J. Connolly
Keyword(s):  
Eighteenth Century ◽  
Recent Article ◽  
Gravitational Attraction ◽  
Matter Theory ◽  
Key Features ◽  
Short Essay ◽  
The Way

In a recent article Fred Ablondi compares the different approaches to occasionalism put forward by two eighteenth-century Newtonians, Colin Maclaurin and Andrew Baxter. The goal of this short essay is to respond to Ablondi by clarifying some key features of Maclaurin's views on occasionalism and the cause of gravitational attraction. In particular, I explore Maclaurin's matter theory, his views on the explanatory limits of mechanism, and his appeals to the authority of Newton. This leads to a clearer picture of the way in which Maclaurin understood gravitational attraction and the workings of nature.

Path Planning of Mobile Robot Using Improved Artificial Bee Colony Algorithm

2020 ◽  
Vol 38 (9A) ◽  
pp. 1384-1395
Author(s):  
Rakaa T. Kamil ◽  
Mohamed J. Mohamed ◽  
Bashra K. Oleiwi
Keyword(s):  
Mobile Robot ◽  
Comparative Research ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Dynamic Control ◽  
Computational Time ◽  
Bee Colony ◽  
Shortest Distance ◽  
Minimum Number ◽  
Cubic Polynomial

A modified version of the artificial Bee Colony Algorithm (ABC) was suggested namely Adaptive Dimension Limit- Artificial Bee Colony Algorithm (ADL-ABC). To determine the optimum global path for mobile robot that satisfies the chosen criteria for shortest distance and collision–free with circular shaped static obstacles on robot environment. The cubic polynomial connects the start point to the end point through three via points used, so the generated paths are smooth and achievable by the robot. Two case studies (or scenarios) are presented in this task and comparative research (or study) is adopted between two algorithm’s results in order to evaluate the performance of the suggested algorithm. The results of the simulation showed that modified parameter (dynamic control limit) is avoiding static number of limit which excludes unnecessary Iteration, so it can find solution with minimum number of iterations and less computational time. From tables of result if there is an equal distance along the path such as in case A (14.490, 14.459) unit, there will be a reduction in time approximately to halve at percentage 5%.

THE GRAVITATIONAL ATTRACTION OF RECTANGULAR MASSES

Survey Review ◽  
1994 ◽  
Vol 32 (251) ◽  
pp. 273-278
Author(s):  
A. C. Ruffhead
Keyword(s):  
Gravitational Attraction
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