11,937 research outputs found
Physical Dissipation and the Method of Controlled Lagrangians
We describe the effect of physical dissipation on stability of
equilibria which have been stabilized, in the absence of damping,
using the method of controlled Lagrangians. This method
applies to a class of underactuated mechanical systems including
âbalanceâ systems such as the pendulum on a cart. Since
the method involves modifying a systemâs kinetic energy metric
through feedback, the effect of dissipation is obscured.
In particular, it is not generally true that damping makes a
feedback-stabilized equilibrium asymptotically stable. Damping
in the unactuated directions does tend to enhance stability,
however damping in the controlled directions must be âreversedâ
through feedback. In this paper, we suggest a choice
of feedback dissipation to locally exponentially stabilize a class
of controlled Lagrangian systems
Dissipation and Controlled Euler-PoincarĂŠ Systems
The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a systemâs energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example,
generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-PoincarĂŠ (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-PoincarĂŠ systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor
Gravitational waves from binary systems in circular orbits: Convergence of a dressed multipole truncation
The gravitational radiation originating from a compact binary system in
circular orbit is usually expressed as an infinite sum over radiative multipole
moments. In a slow-motion approximation, each multipole moment is then
expressed as a post-Newtonian expansion in powers of v/c, the ratio of the
orbital velocity to the speed of light. The bare multipole truncation of the
radiation consists in keeping only the leading-order term in the post-Newtonian
expansion of each moment, but summing over all the multipole moments. In the
case of binary systems with small mass ratios, the bare multipole series was
shown in a previous paper to converge for all values v/c < 2/e, where e is the
base of natural logarithms. In this paper, we extend the analysis to a dressed
multipole truncation of the radiation, in which the leading-order moments are
corrected with terms of relative order (v/c)^2 and (v/c)^3. We find that the
dressed multipole series converges also for all values v/c < 2/e, and that it
coincides (within 1%) with the numerically ``exact'' results for v/c < 0.2.Comment: 9 pages, ReVTeX, 1 postscript figur
Development of an algebraic turbulence model for analysis of propulsion flows
A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC
Effects of long-chord acoustically treated stator vanes on fan noise. 2: Effect of acoustical treatment
A set of long chord stator vanes was designed to replace the vanes in an existing fan stage. The long chord stator vanes consisted of a turning section and axial extension pieces, all of which incorporated acoustic damping material. The long chord stator vanes were tested in two lengths, with the long version giving more noise reduction than the short, primarily because of the additional lining material. The noise reduction achieved with the acoustically treated long chord stator vanes was compared with the reduction achieved by an acoustically treated exhaust splitter. The long chord stator was at least as good as the splitter as a method for incorporating acoustic lining material. In addition, comparing an acoustic three ring inlet and an acoustic wall-only inlet discloses that the wall-only inlet could be used in an engine where the noise reduction requirements are not too stringent
Effects of long-chord acoustically treated stator vanes on fan noise. 1: Effect of long chord (taped stator)
A set of long-chord stator vanes was designed to replace the vanes in an existing fan stage. The long vanes consisted of a turning section and axial extension pieces, both of which incorporated acoustic damping material. The acoustic damping material was made inactive for these tests by covering with metal tape, and the stator vanes were tested in three length configurations. Compared to the values for the original stage, broadband noise was reduced in the middle to high frequencies with the long stator vanes, but a broadband noise increase was observed at the low frequencies. No change was observed in the blade passage tone, but some aft end reduction in the overtones was observed
Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
Starting from a microscopic tight-binding model and using second order
perturbation theory, we derive explicit expressions for the intrinsic and
Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band
structure of an isolated graphene sheet. The Rashba interaction parameter is
first order in the atomic carbon spin-orbit coupling strength and first
order in the external electric field perpendicular to the graphene plane,
whereas the intrinsic spin-orbit interaction which survives at E=0 is second
order in . The spin-orbit terms in the low-energy effective Hamiltonian
have the form proposed recently by Kane and Mele. \textit{Ab initio} electronic
structure calculations were performed as a partial check on the validity of the
tight-binding model.Comment: 5 pages, 2 figures; typos corrected, references update
STABILIZATION OF THREE-DIMENSIONAL COLLECTIVE MOTION
peer reviewedThis paper proposes a methodology to stabilize relative equilibria in a model of
identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group
structure of the resulting dynamical system, the stabilization problem is reduced to a consensus
problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical
formations. We first derive the stabilizing control laws in the presence of all-to-all communication.
Providing each agent with a consensus estimator, we then extend the results to a general setting that
allows for unidirectional and time-varying communication topologies
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