scholarly journals BESSEL FUNCTIONS FOR AXISYMMETRIC ELASTICITY PROBLEMS OF THE ELASTIC HALF SPACE SOIL: A POTENTIAL FUNCTION METHOD

2017 ◽  
Vol 36 (3) ◽  
pp. 773-781
Author(s):  
CC Ike ◽  
HN Onah ◽  
CU Nwoji
Keyword(s):  
Potential Function ◽  
Bessel Functions ◽  
Soil Mass ◽  
Point Load ◽  
Potential Functions ◽  
Field Equations ◽  
Unknown Parameters ◽  
Order Zero ◽  
Elasticity Problems ◽  
Axisymmetric Elasticity

Elasticity problems are formulated using displacement methods or stress methods. In this paper a displacement formulation of axisymmetric elasticity problem is presented. The formulation uses the Boussinesq– Papkovich – Neuber potential function. The problem is then solved by assuming Boussinesq – Papkovich - Neuber potential functions in the form of Bessel functions of order zero and of the first kind. The potential functions are then made to satisfy the governing field equations and the associated boundary conditions for the particular problem of a point load at the origin of the semi-infinite linear elastic isotropic soil mass. The unknown parameters of the function are thus determined and used to find the stresses, strains and displacement fields in the loaded soil. The results obtained were identical with the results obtained by Boussinesq. http://dx.doi.org/10.4314/njt.v36i3.16

The derivation of the rotational potential function from atom–atom potentials. III. Borohydride compounds

1988 ◽  
Vol 66 (4) ◽  
pp. 791-793 ◽  
Author(s):  
David Smith
Keyword(s):  
Transition Temperature ◽  
Experimental Method ◽  
Potential Function ◽  
Ground Level ◽  
Potential Functions ◽  
The Difference ◽  
Level Degeneracy ◽  
Entropy Of Transition ◽  
Good Agreement

The rotational potential functions for the borohydride ion embedded in potassium and rubidium halides are derived from atom–atom potentials of the Buckingham (exp-6) type. The librational frequencies computed from the potential functions are in good agreement with the observed frequencies. The potential functions for rubidium and potassium borohydrides derived from the atom–atom potentials yield librational frequencies that are about 10% higher than the observed values. Since the entropy of transition for potassium and rubidium borohydrides is less than expected, there is a possibility that there is some ordering of the borohydride ions above the transition temperature. An experimental method is presented for studying the ordering of the borohydride ions based on the difference in the ground level degeneracy of a tetrahedral ion in ordered and disordered states.

Control of Multiple Mobile Agents Via Artificial Potential Functions and Random Motion

2007 ◽  
Author(s):  
Manish Kumar ◽  
Devendra P. Garg ◽  
Randy Zachery
Keyword(s):  
Potential Function ◽  
Mobile Agents ◽  
Formation Control ◽  
Cluster Formation ◽  
Limited Range ◽  
Random Motion ◽  
Potential Functions ◽  
Random Behavior ◽  
Artificial Potential Function ◽  
Multiple Mobile Agents

This paper investigates the effectiveness of designed random behavior in cooperative formation control of multiple mobile agents. A method based on artificial potential functions provides a framework for decentralized control of their formation. However, it implies heavy communication costs. The communication requirement can be replaced by onboard sensors. The onboard sensors have limited range and provide only local information, and may result in the formation of isolated clusters. This paper proposes to introduce a component representing random motion in the artificial potential function formulation of the formation control problem. The introduction of the random behavior component results in a better chance of global cluster formation. The paper uses an agent model that includes both position and orientation, and formulates the dynamic equations to incorporate that model in artificial potential function approach. The effectiveness of the proposed method is verified via extensive simulations performed on a group of mobile agents and leaders.

Axisymmetric elasticity problems

2022 ◽  
pp. 397-418
Author(s):  
Muhsin J. Jweeg ◽  
Muhannad Al-Waily ◽  
Kadhim Kamil Resan
Keyword(s):  
Elasticity Problems ◽  
Axisymmetric Elasticity

Constrained on-board attitude control using gas jet thrusters

1999 ◽  
Vol 103 (1030) ◽  
pp. 549-556 ◽  
Author(s):  
G. Radice ◽  
C. R. Mclnnes
Keyword(s):  
Potential Function ◽  
Attitude Control ◽  
Computational Effort ◽  
Potential Functions ◽  
Geometric Configuration ◽  
Gas Jet ◽  
New Approach ◽  
Safety Critical ◽  
Current Attitude ◽  
Lyapunov’S Theorem

Abstract This paper analyses a new approach utilising potential functions to autonomously control constrained attitude slew manoeuvres using gas jet thrusters. The method hinges on defining a potential function from the geometric configuration of the satellite's current attitude, the final target attitude and any pointing constraint which may be present. It will be demonstrated that complex path shaping and planning can be achieved using little computational effort. The method is mathematically validated using Lyapunov's theorem, and so can be considered for safety critical applications.

Modeling of Elastically Coupled Bodies: Part I—General Theory and Geometric Potential Function Method

1998 ◽  
Vol 120 (4) ◽  
pp. 496-500 ◽  
Author(s):  
Ernest D. Fasse ◽  
Peter C. Breedveld
Keyword(s):  
General Theory ◽  
Potential Energy ◽  
Potential Function ◽  
Geometric Modeling ◽  
Function Method ◽  
Rigid Bodies ◽  
Potential Functions ◽  
Energy Functions ◽  
Automatic Computation ◽  
Potential Energy Functions

This paper looks at spatio-geometric modeling of elastically coupled rigid bodies. Desirable properties of compliance families are defined (sufficient diversity, parsimony, frame-indifference, and port-indifference). A novel compliance family with the desired properties is defined using geometric potential energy functions. The configuration-dependent wrenches corresponding to these potential functions are derived in a form suitable for automatic computation.

The general axially symmetric static solution of Einstein’s vacuum field equations

1982 ◽  
Vol 382 (1783) ◽  
pp. 467-470 ◽  
Keyword(s):  
General Solution ◽  
Potential Function ◽  
Line Element ◽  
Static Solution ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Axis Of Symmetry ◽  
Axisymmetric Solutions ◽  
Associated Function

The general solution in closed form, including all the static axisymmetric solutions of Weyl, is presented in the canonical coordinates ρ and z of his line element. This general solution is constructed from an arbitrary function f ( z ), which coincides with his potential function along the axis of symmetry. To illustrate how the solution may be used, a particular function f , one resulting from a Newtonian solution, is used to find both the potential function and its associated function in the line element.

On different parameterisation methods to analyse spacecraft attitude manoeuvres in the presence of attitude constraints

2007 ◽  
Vol 111 (1119) ◽  
pp. 335-342 ◽  
Author(s):  
G. Radice ◽  
M. Casasco
Keyword(s):  
Potential Function ◽  
Function Method ◽  
Potential Functions ◽  
Spacecraft Attitude ◽  
Modified Rodrigues Parameters ◽  
Current Attitude ◽  
Definition Of ◽  
Potential Function Method

Abstract This paper analyses and compares two different attitude representations, using quaternions and modified Rodrigues parameters, in the context of the potential function method applied to autonomously control constrained attitude slew manoeuvres. This method hinges on the definition of novel Lyapunov potential functions in terms of the attitude parameters representing the current attitude, the goal attitude and any pointing constraints, which may be present. It proves to be successful in forcing the satellite to achieve the desired attitude while at the same time avoiding the pointing constraints. A linearised version of the modified Rodrigues parameterisation is also introduced and analysed. Finally advantages and drawbacks of all attitude representations are discussed.

The Remainders in the Asymptotic Expansions of Certain Bessel Functions

1930 ◽  
Vol 26 (2) ◽  
pp. 145-151 ◽  
Author(s):  
D. Burnett
Keyword(s):  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Asymptotic Series ◽  
Order Zero ◽  
Absolute Value

The usual methods of investigation of asymptotic expansions of the various types of Bessel Functions show that the remainder is less in absolute value than the first term neglected. A more refined result was obtained by Stieltjes for K0(x) and certain other functions of order zero; he found an asymptotic series for the remainder and showed that the error due to stopping at one of the smallest terms is of the order of half the first term neglected. Watson notes that it would be of some interest to obtain corresponding results for functions of any order, and this is the object of this note. The method is quite different from that of Stieltjes.

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