Non-linear orbit determination methods

Nonlinear correction method for orbit determination using range, azimuth, and elevation dat

Sound propagation through nonuniform ducts

Methods of determining the transmission and attenuation of sound propagating in nonuniform ducts with and without mean flows are discussed. The approaches reviewed include purely numerical techniques, quasi-one-dimensional approximations, solutions for slowly varying cross sections, solutions for weak wall undulations, approximation of the duct by a series of stepped uniform cross sections, variational methods and solutions for the mode envelopes

Kinematics of foldable discrete space cranes

Exact kinematic description of a NASA proposed prototype foldable-deployable discrete space crane are presented. A computer program is developed which maps the geometry of the crane once controlling parameters are specified. The program uses a building block type approach in which it calculates the local coordinates of each repeating cell and then combines them with respect to a global coordinates system

Effect of streamwise vortices on Tollmien-Schlichting waves

The method of multiple scales is used to determine a first order uniform expansion for the effect of counter rotating steady streamwise vortices in growing boundary layers on Tollmien-Schlichting waves. The results show that such vortices have a strong tendency to amplify three dimensional Tollmien-Schlichting waves having a spanwise wavelength that is twice the wavelength of the vortices. An analytical expression is derived for the growth rates of these waves. These growth rates increase linearly with increasing amplitudes of the vortices

Nonlinear propagation of a wave packet in a hard-walled circular duct

The method of multiple scales is used to derive a nonlinear Schroedinger equation for the temporal and spatial modulation of the amplitudes and the phases of waves propagating in a hard-walled circular duct. This equation is used to show that monochromatic waves are stable and to determine the amplitude dependance of the cut off frequencies

Parametric resonances in electrostatically interacting carbon nanotube arrays

We study, numerically and analytically, a model of a one-dimensional array of carbon nanotube resonators in a two-terminal configuration. The system is brought into resonance upon application of an AC-signal superimposed on a DC-bias voltage. When the tubes in the array are close to each other, electrostatic interactions between tubes become important for the array dynamics. We show that both transverse and longitudinal parametric resonances can be excited in addition to primary resonances. The intertube electrostatic interactions couple modes in orthogonal directions and affect the mode stability.Comment: 11 pages, 12 figures, RevTeX

The stability of motion of satellites with cavities partially filled with liquid

The stability and time dependent motion of a spinning satellite, simulated by a rigid body with a cavity partially filled with liquid is examined. The problem formulation, consisting of the boundary-value problem for the liquid and moment equations for the entire system is presented. Because of large Reynold's numbers involved, viscosity effects are negligible everywhere except for a thin boundary layer near the wetted surface. Using a boundary-layer analysis, the effect of the boundary layer is replaced by modified boundary conditions for the liquid. The solution of the differential equations for the inviscid problem is solved in closed form. A semi-analytical numerical solution of the inviscid equations subject to the viscous boundary condition has proved unsucessful

Nonlinear interaction of waves in boundary-layer flows

First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies w2 is twice the other frequency w1. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction. For the case of three waves, a strong nonlinear interaction exists when w3 = w2- w1. This combination resonance causes the amplitude of the wave with the difference frequency w3 to multiply many times in magnitude in a short distance even if it is damped in the absence of the interaction. The initial amplitudes play a dominant role in determining the changes in the amplitudes of the waves in both of these mechanisms

On the variational homotopy perturbation method for nonlinear oscillators

In this paper we discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators . We show that the main equations are inconsistent and for that reason the results may be of scarce utility

Algebraically growing waves in ducts with sheared mean flow

Standing or traveling waves which vary algebraically with the axial distance in uniform ducts with sheared mean velocity profiles are investigated. The results show that such waves are not possible for ducts with uniform cross sections and fully developed mean flows