Optimal symmetric flight with an intermediate vehicle model

Optimal flight in the vertical plane with a vehicle model intermediate in complexity between the point-mass and energy models is studied. Flight-path angle takes on the role of a control variable. Range-open problems feature subarcs of vertical flight and singular subarcs. The class of altitude-speed-range-time optimization problems with fuel expenditure unspecified is investigated and some interesting phenomena uncovered. The maximum-lift-to-drag glide appears as part of the family, final-time-open, with appropriate initial and terminal transient exceeding level-flight drag, some members exhibiting oscillations. Oscillatory paths generally fail the Jacobi test for durations exceeding a period and furnish a minimum only for short-duration problems

Analytic Construction of Periodic Orbits in the Restricted Three-Body Problem

This dissertation explores the analytical solution properties surrounding a nominal periodic orbit in two different planes, the plane of motion of the two primaries and a plane perpendicular to the line joining the two primaries, in the circular restricted three-body problem. Assuming motion can be maintained in the plane and motion of the third body is circular, Jacobi\u27s integral equation can be analytically integrated, yielding a closed-form expression for the period and path expressed with elliptic integral and elliptic function theory. In this case, the third body traverses a circular path with nonuniform speed. In a strict sense, the in-plane assumption cannot be maintained naturally. However, there may be cases where the assumption is approximately maintained over a finite time period. More importantly, the nominal solution can be used as the basis for an iterative analytical solution procedure for the three dimensional periodic trajectory where corrections are computable in closed-form. In addition, the in-plane assumption can be strictly enforced with the application of modulated thrust acceleration. In this case, the required thrust control inputs are found to be nonlinear functions in time. Total velocity increment, required to maintain the nominal orbit, for one complete period of motion of the third body is expressed as a function of the orbit characteristics

Fully nonlinear interfacial waves in a bounded two-fluid system

We study the nonlinear flow which results when two immiscible inviscid incompressible fluids of different densities and separated by an interface which is free to move and which supports surface tension, are caused to flow in a straight infinite channel. Gravity is taken into consideration and the velocities of each phase can be different, thus giving rise to the Kelvin-Helmholtz instability. Our objective is to study the competing effects of the Kelvin-Helmholtz instability coupled with a stably or unstably stratified fluid system (Rayleigh-Taylor instability) when surface tension is present to regularize the dynamics. Our approach involves the derivation of two-and three-dimensional model evolution equations using long-wave asymptotics and the ensuing analysis and computation of these models. In addition, we derive the appropriate Birkhoff-Rott integro-differential equation for two-phase inviscid flows in channels of arbitrary aspect ratios. A long wave asymptotic analysis is undertaken to develop a theory for fully nonlinear interfacial waves allowing amplitudes as large as the channel thickness. The result is a set of evolution equations for the interfacial shape and the velocity jump across the interface. Linear stability analysis reveals that capillary forces stabilize short-wave disturbances in a dispersive manner and we study their effect on the fully nonlinear dynamics described by our models. In the case of two-dimensional interfacial deflections, traveling waves of permanent form are constructed and it is shown that solitary waves are possible for a range of physical parameters. All solitary waves are expressed implicitly in terms of incomplete elliptic integrals of the third kind. When the upper layer has zero density, two explicit solitary-wave solutions have been found whose amplitudes are equal to h/4 or h/9 where 2h is the channel thickness. In the absence of gravity, solitary waves are not possible but periodic ones are. Numerically constructed traveling and solitary waves are given for representative physical parameters. The initial value problem for the partial differential equations is also addressed numerically in periodic domains, and the regularizing effect of surface tension is investigated. In particular, when surface tension is absent it is shown that the system of governing evolution equations terminates in a singularity after a finite time. This is achieved by studying a 2 x 2 system of nonlinear conservation laws in the complex plane and by numerical solution of the evolution equations. The analysis shows that a sinusoidal perturbation of the flat interface and a cosine perturbation to the unit velocity jump across the interface, develop a singularity at time tc = ln 1/ε+0 (ln(ln 1/ε)) where ε is the initial amplitude of the disturbances. This result is asymptotic for small ε and is derived by studying the asymptotic form of the flow characteristics in the complex plane. We also derive the analogous three-dimensional evolution equations by assuming that the wavelengths in the principal horizontal directions are large compared to the channel thickness. Surface tension is again incorporated to regularize short-wave Kelvin-Helmholtz instabilities and the equations are solved numerically subject to periodic boundary conditions. Evidence of singularity formation is found. In particular, we observe that singularities occur at isolated points starting from general initial conditions. This finding is consistent with numerical studies of unbounded three-dimensional vortex sheets (see Introduction for a discussion and references). In the final part of this work we consider the vortex-sheet formulation of the exact nonlinear two-dimensional flow of a vortex sheet which is bounded in a channel. We derive a Birkhoff-Rott type integro-differential evolution equation for the velocity of the interface in terms of the vorticity as well as the evolution equation for the unnormalized vortex sheet strength. For the case of a spatially periodic vortex sheet, this Birkhoff-Rott type equation is written in terms of Jacobi\u27s functions. The equation is shown to recover the limits of unbounded and non-periodic flows which are known in the literature

Nonlinear transient analysis based on power waves and state variables

Muhammad Ershadul Kabir was born in Chittagong, Bangladesh on July 15, 1982. He received the Bachelor of Science in Electrical and Electronic Engineering from Bangladesh University of Engineering and Technology (BUET) in Dhaka, Bangladesh in June, 2005. From July, 2005 to August, 2008 he worked in Motorola Telecommunication Bangladesh Pvt. Ltd. as System Engineer. During this time, he designed many SDH and PDH communication networks for different Wireless and PSTN operators in Bangladesh. In September 2008 he enrolled in the Masters program of Electrical and Computer Engineering in Lakehead University and move in Canada along with his wife. His research interests include Computer Aided Design (CAD) of Circuit and systems, Simulation Techniques and Algorithms, Parallel computing system and parallel Implementation of CAD tools, Implementation of CAD tools in Graphics processing unit (GPU), Analog and mixed-signal circuit design, VLSI circuit design. He is a student member of the Institute of Electrical and Electronics Engineers (IEEE)

Uniqueness theorems for a class of singular partial differential equations

Of fundamental importance in physics are problems whose mathematical formulation requires at least three dimensions. Since in many ways one and two dimensional problems are easier to handle, one of the major efforts of mathematicians has been to reduce three dimensional problems to those of lower dimensions. Fourier analysis, separation of variables, integral transforms, and the introduction of various kinds of axial symmetry are some of the more familiar methods that have been devised with this aim in mind. This thesis is concerned with the study of the two dimensional equations that result when Fourier analysis is applied to the three dimensional Helmholtz or reduced wave equation

Structural Analysis and Matrix Interpetive System /SAMIS/ program Technical report, Feb. - Aug. 1966

Development of characteristic equations and error analysis for computer programs contained in structural analysis and matrix interpretive syste

Image-based ranging and guidance for rotorcraft

This report documents the research carried out under NASA Cooperative Agreement No. NCC2-575 during the period Oct. 1988 - Dec. 1991. Primary emphasis of this effort was on the development of vision based navigation methods for rotorcraft nap-of-the-earth flight regime. A family of field-based ranging algorithms were developed during this research period. These ranging schemes are capable of handling both stereo and motion image sequences, and permits both translational and rotational camera motion. The algorithms require minimal computational effort and appear to be implementable in real time. A series of papers were presented on these ranging schemes, some of which are included in this report. A small part of the research effort was expended on synthesizing a rotorcraft guidance law that directly uses the vision-based ranging data. This work is discussed in the last section

Symmetries of differential equations. IV

By an application of the geometrical techniques of Lie, Cohen, and Dickson it is shown that a system of differential equations of the form [x^(r_i)]_i = F_i(where r_i > 1 for every i = 1 , ... ,n) cannot admit an infinite number of pointlike symmetry vectors. When r_i = r for every i = 1, ... ,n, upper bounds have been computed for the maximum number of independent symmetry vectors that these systems can possess: The upper bounds are given by 2n_ 2 + nr + 2 (when r> 2), and by 2n_2 + 4n + 2 (when r = 2). The group of symmetries of ͞x^r = ͞0 (r> 1) has also been computed, and the result obtained shows that when n > 1 and r> 2 the number of independent symmetries of these equations does not attain the upper bound 2n _2 + nr + 2, which is a common bound for all systems of differential equations of the form ͞x^r = F[t, ͞x, ... , ͞x^(r - 1 )] when r> 2. On the other hand, when r = 2 the first upper bound obtained has been reduced to the value n^2 + 4n + 3; this number is equal to the number of independent symmetry vectors of the system ͞x= ͞0, and is also a common bound for all systems of the form ͞x = ͞F (t ,͞x, ‾̇x)

Glosarium Matematika

273 p.; 24 cm