Nonlinear dynamics of a satellite with deployable solar panel arrays

The multibody dynamics of a satellite in circular orbit, modeled as a central body with two hinge-connected deployable solar panel arrays, is investigated. Typically, the solar panel arrays are deployed in orbit using preloaded torsional springs at the hinges in a near symmetrical accordion manner, to minimize the shock loads at the hinges. There are five degrees of freedom of the interconnected rigid bodies, composed of coupled attitude motions (pitch, yaw and roll) of the central body plus relative rotations of the solar panel arrays. The dynamical equations of motion of the satellite system are derived using Kane's equations. These are then used to investigate the dynamic behavior of the system during solar panel deployment via the 7-8th-order Runge-Kutta integration algorithms and results are compared with approximate analytical solutions. Chaotic attitude motions of the completely deployed satellite in circular orbit under the influence of the gravity-gradient torques are subsequently investigated analytically using Melnikov's method and confirmed via numerical integration. The Hamiltonian equations in terms of Deprit's variables are used to facilitate the analysis. (C) 2003 Published by Elsevier Ltd.

Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Decentralized control design for nonlinear plants: a v-metric approach

In this paper, a new v-metric based approach is proposed to design decentralized controllers for multi-unit nonlinear plants that admit a set of plant decompositions in an operating space. Similar to the gap metric approach in literature, it is shown that the operating space can also be divided into several subregions based on a v-metric indicator, and each of the subregions admits the same controller structure. A comparative case study is presented to display the advantages of proposed approach over the gap metric approach. (C) 2000 Elsevier Science Ltd. All rights reserved.

Recruitment of single human low-threshold motor units with increasing loads at different muscle lengths

We investigated the recruitment behaviour of low threshold motor units in flexor digitorum superficialis by altering two biomechanical constraints: the load against which the muscle worked and the initial muscle length. The load was increased using isotonic (low load), loaded dynamic (intermediate load) and isometric (high load) contractions in two studies. The initial muscle position reflected resting muscle length in series A, and a longer length with digit III fully extended in series B. Intramuscular EMG was recorded from 48 single motor units in 10 experiments on five healthy subjects, 21 units in series A and,27 in series B, while subjects performed ramp up, hold and ramp down contractions. Increasing the load on the muscle decreased the force, displacement and firing rate of single motor units at recruitment at shorter muscle lengths (P < 0.001, dependent t-test). At longer muscle lengths this recruitment pattern was observed between loaded dynamic and isotonic contractions, but not between isometric and loaded dynamic contractions. Thus, the recruitment properties of single motor units in human flexor digitorum superficialis are sensitive to changes in both imposed external loads and the initial length of the muscle. (C) 2003 Elsevier Ltd. All rights reserved.

Investment prioritization based on broadscale spatial budgeting to meet downstream targets for suspended sediment loads

On the basis of a spatially distributed sediment budget across a large basin, costs of achieving certain sediment reduction targets in rivers were estimated. A range of investment prioritization scenarios were tested to identify the most cost-effective strategy to control suspended sediment loads. The scenarios were based on successively introducing more information from the sediment budget. The relationship between spatial heterogeneity of contributing sediment sources on cost effectiveness of prioritization was investigated. Cost effectiveness was shown to increase with sequential introduction of sediment budget terms. The solution which most decreased cost was achieved by including spatial information linking sediment sources to the downstream target location. This solution produced cost curves similar to those derived using a genetic algorithm formulation. Appropriate investment prioritization can offer large cost savings because the magnitude of the costs can vary by several times depending on what type of erosion source or sediment delivery mechanism is targeted. Target settings which only consider the erosion source rates can potentially result in spending more money than random management intervention for achieving downstream targets. Coherent spatial patterns of contributing sediment emerge from the budget model and its many inputs. The heterogeneity in these patterns can be summarized in a succinct form. This summary was shown to be consistent with the cost difference between local and regional prioritization for three of four test catchments. To explain the effect for the fourth catchment, the detail of the individual sediment sources needed to be taken into account.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.