Showing papers by "Vaughn College of Aeronautics and Technology published in 1964"

On the integration of Maxwell's equations, and charge and dipole fields

Abstract: It is shown how the direct integration of Maxwell's equations for free space may be accomplished by using a four-dimensional integral identity constructed for this purpose. The method is applied to the calculation of the electromagnetic fields of moving electric charges, and electric and magnetic dipoles. INTRODUJCTION In many problems in mathematical physics where the dependent variables of physical interest satisfy partial differential equations, one or more of these equations is homogeneous, and potential functions can be introduced from which the dependent variables can be deduced by differentiation. But in other problems, the differential equations are inhomogeneous and no potential functions exist, in which case it is useful to have a method for solving the equations directly by using suitable Green functions: also, even when potential functions do exist, it is of theoretical, if not of practical, interest to have a direct method of solution. In the case of Maxwell's equations, direct methods of solution have been used by other authors when the time-variations of the electromagnetic field are harmonic (cf. Stratton I 941) and the time co-ordinate can be separated, but direct methods when the time is present as an independent variable have not received much attention. Some years ago, the author published a method for the direct integration of the linearized vector equations for the velocity in steady flow of perfect gases (Ward I952). In that case the equations were written as two inhomogeneous first-order equations for the velocity, and it was possible to use a previously known vector integral identity to perform the function of a Green identity. Subsequently, this method was generalized to deal with the linearized equations for unsteady flow of perfect gases (Ward i963), the treatment being four-dimensional instead of threedimensional, and the required integral identity being a simple generalization of that used for steady flows. In both problems, it was convenient to write the vector equations of motion in symmetrical form with respect to the independent variables, and this seemed to lead necessarily to redundancy in the systems of equations, in the sense that they were equivalent to more scalar equations than there were scalar components of the vector variables, but of course the systems were consistent among themselves. The same order of ideas can be applied to the problem of integrating other systems of vector differential equations, and an application to Maxwell's equations for the electromagnetic field is treated in this paper. The appropriate symmetrical fourdimensional form of Maxwell's equations is already established (cf. Stratton I 941), the dependent variable being an anti-symmetrical tensor or six-vector. It is interesting to note that this system of equations is also redundant, being equivalent to

A preliminary study of a capstan lathe

Abstract: SUMMARY Possible approaches to the study of the ergonomics of machine tool design are discussed and a particular case is described in which the operation of the controls of a capstan lathe was studied, various modifications were instituted and a preliminary evaluation of one of them was attempted.

The effect of catalytic surfaces on stagnation point heat transfer in partially dissociated flows

Abstract: Experimental results are presented, which show that the heat transfer rate to a silicon monoxide coated surface is less than that to a platinum surface when the flow outside the boundary layer is partially dissociated. It has been inferred, from these results, that the recombination coefficient for the platinum surface used in these tests, lies between 6 × 10 −4 and 6 × 10 −3 . It has also been concluded, from one particular set of tests, that the flow in the stagnation region was not in equilibrium and was only half dissociated. Suggestions are made for the construction of a probe to measure atom concentrations and relaxation times in short duration flows.

Comment on “The Load Distribution on a Polynomial Mean Line and the Converse”

Abstract: I am grateful to Mr. Llewelyn for pointing out the slip in equation (3) of reference 1. In considering a particular case of the polynomial camber line I did have to evaluate a number of integrals of the kind but the process is not as laborious as perhaps Mr. Llewelyn implies for there is a simple recurrence relation between integrals of this kind.