Structural Dynamics, Stability, and Control of Helicopters

The dynamic synthesis of gyroscopic structures consisting of point-connected substructures is investigated. The objective is to develop a mathematical model capable of an adequate simulation of the modal characteristics of a helicopter using a minimum number of degrees of freedom. The basic approach is to regard the helicopter structure as an assemblage of flexible substructures. The variational equations for the perturbed motion about certain equilibrium solutions are derived. The discretized variational equations can be conveniently exhibited in matrix form, and a great deal of information about the system modal characteristics can be extracted from the coefficient matrices. The derivation of the variational equations requires a monumental amount of algebraic operations. To automate this task a symbolic manipulation program on a digital computer is developed

Dynamics, Stability, and Foresight in the Shapley-Scarf Housing Market

While most of the literature starting with Shapley and Scarf (1974) have considered a static exchange economy with indivisibilities, this paper studies the dynamics of such an economy. We find that both the dynamics generated by competitive equilibrium and the one generated by weakly dominance relation, converge to a set of allocations we define as strictly stable, which we can show to exist. Moreover, we show that even when only pairwise exchanges between two traders are allowed, the strictly stable allocations are attained eventually if traders are sufficiently farsighted.Indivisible Goods Market, Dynamics, Competitive Allocation, Strict Core, Foresight, Stable Set

Movement of equilibrium of Cournot duopoly and the visualization of bifurcations of its adjustment dynamics

This paper deals with the analytical and graphical representation of the bifurcations appearing from the adjustment dynamics of a 2- player Cournot duopoly, proposed by Puu (1997). We establish admissibility conditions on the initial state of the adjustment dynamics and visualize the dynamics in the space of orbits.Bifurcation surfaces, Chaos, Cournot, Duopoly, Nonlinear dynamics, Stability.

Cascading failures: dynamics, stability and control

We develop a dynamic model of cascading failures in a financial network whereby cross-holdings are viewed as feedback, external assets investments as inputs and failure penalties as static nonlinearities. We provide sufficient milder and stronger conditions for the system to be a positive one, and study equilibrium points and stability. Stability implies absence of cascades and convergence of market values to constant values. We provide a constructive method for control design to obtain stabilizing market investments in the form of feedback-feedforward control inputs

Stabilization via generalized homogeneous approximations

We introduce a notion of generalized homogeneous approximation at the origin and at infinity which extends the classical notions and captures a large class of nonlinear systems, including (lower and upper) triangular systems. Exploiting this extension and although this extension does not preserve the basic properties of the classical notion, we give basic results concerning stabilization and robustness of nonlinear systems, by designing a homogeneous (in the generalized sense) feedback controller which globally asymptotically stabilizes a chain of power integrators and makes it the dominant part at infinity and at the origin (in the generalized sense) of the dynamics. Stability against nonlinear perturbation follows from domination arguments

Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in diamond anvil cell. Application to the stability study of AlPdMn

We report an innovative high pressure method combining the diamond anvil cell device with the technique of picosecond ultrasonics. Such an approach allows to accurately measure sound velocity and attenuation of solids and liquids under pressure of tens of GPa, overcoming all the drawbacks of traditional techniques. The power of this new experimental technique is demonstrated in studies of lattice dynamics, stability domain and relaxation process in a metallic sample, a perfect single-grain AlPdMn quasicrystal, and rare gas, neon and argon. Application to the study of defect-induced lattice stability in AlPdMn up to 30 GPa is proposed. The present work has potential for application in areas ranging from fundamental problems in physics of solid and liquid state, which in turn could be beneficial for various other scientific fields as Earth and planetary science or material research

Distributed Control of Positive Systems

A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage functions can be used instead of quadratic ones. This paper shows how such methods can be used for synthesis of distributed controllers. It also shows that stability and performance of such control systems can be verified with a complexity that scales linearly with the number of interconnections. Several results regarding scalable synthesis and verfication are derived, including a new stronger version of the Kalman-Yakubovich-Popov lemma for positive systems. Some main results are stated for frequency domain models using the notion of positively dominated system. The analysis is illustrated with applications to transportation networks, vehicle formations and power systems

Multiscale foam dynamics: stability mechanisms in salty solutions

An oilfield is a region that is generally part of a sedimentary geological formation, made up of porous and permeable rocks, and bounded by impermeable barriers. A fluid is injected to displace the trapped oil. Most fluids are less viscous than the oil, where they are prone to pierce through the porous rock. When pressurized in an attempt to displace the oil, they pierce through the oil in an instability known as viscous fingering. Therefore, identifying appropriate candidate fluids is an essential step in improving oil recovery rate. In this thesis work, an aqueous foam is chosen as a candidate fluid for investigation. A collection of free drainage studies has been conducted to gain deeper understanding of foams’ ageing processes at different temporal and spatial scales. A commercially available nonionic surfactant, Triton X-100, has been used to produce foams. First, container effects are investigated to study how bulk foam dynamics change in differently shaped and sized containers. Second, an optical imaging system is developed to study the multi-scale dynamics of aqueous foam. Finally, using the newly developed optical imaging system, experiments at different salinities are conducted to study the salinity dependence on foam stability at different temporal and spatial scales. This information will likely impact the design of foam stability testing methods and contribute to the understanding of high salinity bubble interactions

Dynamics stability derivatives of space shuttle orbiter obtained from wind-tunnel and approach and landing flight tests

A comparison was made between ground facility measurements, the aerodynamic design data book values, and the dynamic damping derivatives extracted from the space shuttle orbiter approach and landing flight tests. The comparison covers an angle of attack range from 2 deg to 10 deg at subsonic Mach numbers. The parameters of pitch, yaw, and roll damping, as well as the yawing moment due to rolling velocity and rolling moment due to yawing velocity are compared