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Low thrust trajectory optimization, using Newton- Raphson method to solve nonlinear two-point boundary value problem
The features of the limb inversion problem that differentiate it from the nadir problem are described; the most important of these are the sharply peaked weighting functions and the nonlinear kernel that arises because the atmosphere is required to be in hydrostatic balance. The problem may be split into two parts: given the pressure at one level and the measured radiances, can the temperatures be retrieved? And how can the pressure be obtained at one level? The second problem is shown to depend on the first, which is solved iteratively. The convergence properties and final accuracies are presented. Inversion to obtain trace constituents is briefly discussed.
It is well-known that a number of steady state problems in fluid mechanics involving systems of nonlinear partial differential equations can be reduced to the problem of solving a single operator equation of the form: v + lambda Av + lambda B(v) = 0, v is the summation of H, lambda is the summation of one-dimensional Euclid space, where H is an appropriate (real or complex) Hilbert space. Here lambda is a typical load parameter, e.g., the Reynolds number, A is a linear operator, and B is a quadratic operator generated by a bilinear form. In this setting many bifurcation and stability results for problems were obtained. A rotating Couette-Poiseuille channel flow was studied, and it showed that, in general, the superposition of a Poiseuille flow on a rotating Couette channel flow is destabilizing.
Aspects of general solution to optimal control problem - boundaries of linear, nonlinear, and saturation modes
Signal and noise problem as solution to nonlinear stochastic differential equations
Differential dynamic programming algorithms of second and first order for optimal control, considering nonlinear unconstrained and constrained problems
Mathematical solution of nonlinear transverse combustion instability problems in thin annular liquid propellant rocket chambers
Three body stellar problem libration calculation using nonlinear mechanics methods, and application to lunar satellite perturbation by earth and lunar gravitational effects
Nonlinear static structural mechanical problems solution, using self correcting initial value formulations
An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering.
A new analytical technique for the solution of nonlinear longitudinal combustion instability problems in rocket combustors is developed. Using relatively little computation time, this technique is capable of predicting the transient and limit cycle behavior of the combustion instability oscillations as well as the disturbance amplitude required to trigger an instability in a linearly stable motor. The limit cycle waveforms are found to exhibit shock wave characteristics for most unstable engine operating conditions. It is shown that the characteristics of the resulting instability are independent of the nature of the initial disturbance and they depend solely upon the engine operating conditions and the characteristics of the unsteady combustion process.
A practical finite element method is presented for geometrically nonlinear (von Karman) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stages of non-linearity. Several different triangular elements are used in explicitly deriving the required tensors.
An approach is developed to the application of the perturbation method for the solution of problems with essential external nonlinearities, based on identification in the boundary condition of a small nonlinear complex which is considered a perturbing function. The solutions obtained in the first approximation with error of 1 to 2% in calculating the unsteady temperature fields are then used to determine the temperature stresses and deformations in solid bodies of classical form.
An effective procedure for NASTRAN was developed that permits any number of substructures of any size to be synthesized for the purpose of developing normal modes of vibration of the complete structural system. The technique is extended to permit modal transient analysis of the subdivided system. This latter procedure permits the use of NASTRAN's ability to include nonlinear forces in the problem. The five-phase process is accomplished using standard NASTRAN rigid formats with problem-independent alter packages and DMAP sequences.
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions. The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave. This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasi-neutral beam results. The relaxation scale in space agrees with neutralization experiments of rarefied ion beams, if the collective momentum transfer between the electron and ion streams is assumed to be of the Buneman type.
One approach to the problem of simplifying complex nonlinear filtering algorithms is through using stratified probability approximations where the continuous probability density functions of certain random variables are represented by discrete mass approximations. This technique is developed in this paper and used to simplify the filtering algorithms developed for the optimum receiver for signals corrupted by both additive and multiplicative noise.
The elastic instability of an internally-pressurized cylindrical tank with a torispherical head is investigated using a triangular, doubly curved, thin-shell finite element. The formulation of the finite element, which is based upon cubic displacement functions and a modified principle of potential energy, is first described. Then, the element is verified by comparing numerical results for the linear, stable analysis to alternative solutions for the same problem. The subsequent instability investigation includes the solution of the linearized problem of equilibrium bifurcation, that is, of the classical eigenvalue problem, and a general nonlinear analysis, based on tracing the nonlinear load-displacement path. The critical pressure, obtained with use of the general nonlinear analysis, agrees closely with an experimental result as well as with a numerical solution stemming from an axisymmetric formulation.