Application of the Conjugate Gradient Method to a Problem on Minimum Time Orbit Transfer

This correspondence considers the problem of optimally controlling the thrust steering angle of an ion-propelled spaceship so as to effect a minimum time coplanar orbit transfer from the mean orbital distance of Earth to mean Martian and Venusian orbital distances. This problem has been modelled as a free terminal time-optimal control problem with unbounded control variable and with state variable equality constraints at the final time. The problem has been solved by the penalty function approach, using the conjugate gradient algorithm. In general, the optimal solution shows a significant departure from earlier work. In particular, the optimal control in the case of Earth-Mars orbit transfer, during the initial phase of the spaceship's flight, is found to be negative, resulting in the motion of the spaceship within the Earth's orbit for a significant fraction of the total optimized orbit transfer time. Such a feature exhibited by the optimal solution has not been reported at all by earlier investigators of this problem.

Analytical method for solving a set of inhomogeneous infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of inhomogeneous infinite simultaneous equations encountered in the analysis of surface acoustic wave propagation along the periodically perturbed surface of a piezoelectric medium.

A critical analysis of the shear difference method

The shear difference method which is commonly used for the separation of normal stresses using photoelastic techniques depends on the step-by-step integration of one of the differential equations of equilibrium. It is assumed that the isoclinic and the isochromatic parameters measured by the conventional methods pertain to the state of stress at the midpoint of the light path. In practice, a slice thin enough for the above assumption to be true and at the same time thick enough to give differences in the shear-stress values over the thickness is necessary. The paper discusses the errors introduced in the isoclinic and isochromatic values by the conventional methods neglecting the variation of stresses along the light path. It is shown that while the error introduced in the measurement of the isochromatic parameter may not be serious, the error caused in the isoclinic measurement may lead to serious errors. Since the shear-difference method involves step-by-step integration the error introduced will be of a cumulative nature.

A method for the experimental evaluation of the acoustic characteristics of an engine exhaust system in the presence of mean flow

The paper deals with an exact analysis of standing waves in an impedance tube with mean flow. A method is offered for the experimental evaluation of the various wave parameters. Navier–Stokes equations have been solved for evaluating the volume velocity taking into account mean flow, viscosity, etc. The engine exhaust system has been characterized as an acoustic source with an acoustic pressure and internal impedance. A method is suggested for the evaluation of these hypothetical parameters using the exhaust pipe as an impedance tube.Subject Classification: [43]85.20; [43]20.40.

A novel method of current efficiency determination

A simple and rapid method, based on the open-circuit decay of potential, is described for the determination of the current efficiency with which metals are electrodeposited. The advantages and disadvantages of the method are discussed.

A Modified Dubins Method for Optimal Path Planning of a Miniature Air Vehicle Converging to a Straight Line Path

This paper presents a Dubins model based strategy to determine the optimal path of a Miniature Air Vehicle (MAV), constrained by a bounded turning rate, that would enable it to fly along a given straight line, starting from an arbitrary initial position and orientation. The method is then extended to meet the same objective in the presence of wind which has a magnitude comparable to the speed of the MAV. We use a modification of the Dubins' path method to obtain the complete optimal solution to this problem in all its generality.

A New Method for the Preparation of Sulphuryl Chloro Fluoride

It has been observed that a suspension of sodium fluoride in boiling acetonitrile could be used for the preparation of fluorine compounds such as silicon tetrafluoride [1], thiophosphoryl fluoride [2], sulphur tetrafluoride [3,4], and fluorocyclophosphazenes [5]. This method, when adopted for the fluorination of sulphuryl chloride [6], it is observed that a mixture of sulphuryl fluoride and sulphuryl chloro fluoride is obtained. On the other hand, when lead fluoride is substituted for sodium fluoride, pure sulphuryl chloro fluoride is evolved. Based on this observation, a new method has been standardised for the preparation of a pure sample of sulphuryl chlorofluoride by fluorinating sulphuryl chloride by lead fluoride in acetonitrile medium.

A numerical method for separation of stresses in photo-orthotropic elasticity

A numerical method is suggested for separation of stresses in photo-orthotropic elasticity using the numerical solution of compatibility equation for orthotropic case. The compatibility equation is written in terms of a stress parameter S analogous to the sum of principal stresses in two-dimensional isotropic case. The solution of this equation provides a relation between the normal stresses. The photoelastic data give the shear stress and another relation between the two normal stresses. The accuracy of the numerical method and its application to practical problems are illustrated with examples.

Analysis of vibration of clamped square plates by the Rayleigh-Ritz method with asymptotic solutions from a modified Bolotin method

Estimates of flexural frequencies of clamped square plates are initially obtained by the modified Bolotin's method. The mode shapes in “each direction” are then determined and the product functions of these mode shapes are used as admissible functions in the Rayleigh-Ritz method. The data for the first twenty eigenvalues in each of the three (four) symmetric groups obtained by the (i) Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are reported here. The Rayleigh estimates are found to be much closer to the true eigenvalues than the Bolotin estimates. The present product functions are found to be much superior to the conventional beam eigenmodes as admissible functions in the Rayleigh-Ritz method of analysis.

Velocity ratio-cum-transfer matrix method for the evaluation of a muffler with mean flow

The paper deals with a method for the evaluation of exhaust muffers with mean flow. A new set of variables, convective pressure and convective mass velocity, have been defined to replace the acoustic variables. An expression for attenuation (insertion loss) of a muffler has been proposed in terms of convective terminal impedances and a velocity ratio, on the lines of the one existing for acoustic filters. In order to evaluate the velocity ratio in terms of convective variables, transfer matrices for various muffler elements have been derived from the basic relations of energy, mass and momentum. Finally, the velocity ratiocum-transfer matrix method is illustrated for a typical straight-through muffler.

The doctrinal method: Incorporating interdisciplinary methods in reforming the law

The doctrinal methodology is in a period of change and transition. Realising that the scope of the doctrinal method is too constricting, academic lawyers are becoming eclectic in their use of research method. In this transitional time, legal scholars are increasingly infusing evidence (and methods) from other disciplines into their reasoning to bolster their reform recommendations. This article considers three examples of the interplay of the discipline of law with other disciplines in the pursuit of law reform. Firstly the article reviews studies on the extent of methodologies and reformist frameworks in PhD research in Australia. Secondly it analyses a ‘snapshot’ of recently published Australian journal articles on criminal law reform. Thirdly, it focuses on the law reform commissions, those independent government committees that play such an important role in law reform in common law jurisdictions. This examination demonstrates that while the doctrinal core of legal scholarship remains intact, legal scholars are endeavouring to accommodate statistics, comparative perspectives, social science evidence and methods, and theoretical analysis, within the legal research framework, in order to provide additional ballast to the recommendations for reform.

Numerical study of heat transfer in laminar film boiling by the finite-difference method

The finite-difference form of the basic conservation equations in laminar film boiling have been solved by the false-transient method. By a judicious choice of the coordinate system the vapour-liquid interface is fitted to the grid system. Central differencing is used for diffusion terms, upwind differencing for convection terms, and explicit differencing for transient terms. Since an explicit method is used the time step used in the false-transient method is constrained by numerical instability. In the present problem the limits on the time step are imposed by conditions in the vapour region. On the other hand the rate of convergence of finite-difference equations is dependent on the conditions in the liquid region. The rate of convergence was accelerated by using the over-relaxation technique in the liquid region. The results obtained compare well with previous work and experimental data available in the literature.

Analytical method for solving a set of infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of infinite simultaneous equations encountered in solving for the electric field of a periodic electrode structure.

Method for evaluation of the acoustical impedance of a black box, with or without mean flow, measuring pressures at fixed positions

The transmission-line or the impedance-tube method for the measurement of the acoustic impedance of any termination involves a search for various minima and maxima of pressure. For this purpose, arrangement has to be made for the microphone to travel along the length of the impedance tube, and this complicates the design of the tube considerably. The present paper discusses a method which consists in evaluating the tube attenuation factor at any convenient frequency by making use of measured SPL's at two (or more) fixed locations with a rigid termination, calculating the tube attenuation factor and wave number at the required frequency of interest with or without mean flow (as applicable), and finally evaluating the impedance of the given termination by measuring and using SPL's at three (or more) fixed locations. Thus, the required impedance tube is considerably smaller in length, simpler in design, easier to manufacture, cheaper in cost and more convenient to use. The design of the tube is also discussed. Incidentally, it is also possible to evaluate the impedance at any low frequency without having to use a larger impedance tube.