346 research outputs found
A method of determining attitude from magnetometer data only
Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress
Magnetometer-only attitude and rate determination for a gyro-less spacecraft
Attitude determination algorithms that requires only the earth's magnetic field will be useful for contingency conditions. One way to determine attitude is to use the time derivative of the magnetic field as the second vector in the attitude determination process. When no gyros are available, however, attitude determination becomes difficult because the rates must be propagated via integration of Euler's equation, which in turn requires knowledge of the initial rates. The spacecraft state to be determined must then include not only the attitude but also rates. This paper describes a magnetometer-only attitude determination scheme with no a priori knowledge of the spacecraft state, which uses a deterministic algorithm to initialize an extended Kalman filter. The deterministic algorithm uses Euler's equation to relate the time derivatives of the magnetic field in the reference and body frames and solves the resultant transcendental equations for the coarse attitude and rates. An important feature of the filter is that its state vector also includes corrections to the propagated rates, thus enabling it to generate highly accurate solutions. The method was tested using in-flight data from the Solar, Anomalous, and Magnetospheric Particles Explorer (SAMPEX), a Small Explorer spacecraft. SAMPEX data using several eclipse periods were used to simulate conditions that may exist during the failure of the on-board digital sun sensor. The combined algorithm has been found effective, yielding accuracies of 1.5 deg in attitude (within even nominal mission requirements) and 0.01 degree per second (deg/sec) in the rates
Advantages of estimating rate corrections during dynamic propagation of spacecraft rates: Applications to real-time attitude determination of SAMPEX
This paper describes real-time attitude determination results for the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX), a gyroless spacecraft, using a Kalman filter/Euler equation approach denoted the real-time sequential filter (RTSF). The RTSF is an extended Kalman filter whose state vector includes the attitude quaternion and corrections to the rates, which are modeled as Markov processes with small time constants. The rate corrections impart a significant robustness to the RTSF against errors in modeling the environmental and control torques, as well as errors in the initial attitude and rates, while maintaining a small state vector. SAMPLEX flight data from various mission phases are used to demonstrate the robustness of the RTSF against a priori attitude and rate errors of up to 90 deg and 0.5 deg/sec, respectively, as well as a sensitivity of 0.0003 deg/sec in estimating rate corrections in torque computations. In contrast, it is shown that the RTSF attitude estimates without the rate corrections can degrade rapidly. RTSF advantages over single-frame attitude determination algorithms are also demonstrated through (1) substantial improvements in attitude solutions during sun-magnetic field coalignment and (2) magnetic-field-only attitude and rate estimation during the spacecraft's sun-acquisition mode. A robust magnetometer-only attitude-and-rate determination method is also developed to provide for the contingency when both sun data as well as a priori knowledge of the spacecraft state are unavailable. This method includes a deterministic algorithm used to initialize the RTSF with coarse estimates of the spacecraft attitude and rates. The combined algorithm has been found effective, yielding accuracies of 1.5 deg in attitude and 0.01 deg/sec in the rates and convergence times as little as 400 sec
Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation
It is shown that the energy of a mode of a classical chaotic field, following
the continuous exponential distribution as a classical random variable, can be
uniquely decomposed into a sum of its fractional part and of its integer part.
The integer part is a discrete random variable (we call it Planck variable)
whose distribution is just the Bose distribution yielding the Planck law of
black-body radiation. The fractional part is the dark part (we call is dark
variable) with a continuous distribution, which is, of course, not observed in
the experiments. It is proved that the Bose distribution is infinitely
divisible, and the irreducible decomposition of it is given. The Planck
variable can be decomposed into an infinite sum of independent binary random
variables representing the binary photons (more accurately photo-molecules or
photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons
follow the Fermi statistics. Consequently, the black-body radiation can be
viewed as a mixture of statistically and thermodynamically independent fermion
gases consisting of binary photons. The binary photons give a natural tool for
the dyadic expansion of arbitrary (but not coherent) ordinary photon
excitations. It is shown that the binary photons have wave-particle
fluctuations of fermions. These fluctuations combine to give the wave-particle
fluctuations of the original bosonic photons expressed by the Einstein
fluctuation formula.Comment: 29 page
Quasi-normal frequencies: Key analytic results
The study of exact quasi-normal modes [QNMs], and their associated
quasi-normal frequencies [QNFs], has had a long and convoluted history -
replete with many rediscoveries of previously known results. In this article we
shall collect and survey a number of known analytic results, and develop
several new analytic results - specifically we shall provide several new QNF
results and estimates, in a form amenable for comparison with the extant
literature. Apart from their intrinsic interest, these exact and approximate
results serve as a backdrop and a consistency check on ongoing efforts to find
general model-independent estimates for QNFs, and general model-independent
bounds on transmission probabilities. Our calculations also provide yet another
physics application of the Lambert W function. These ideas have relevance to
fields as diverse as black hole physics, (where they are related to the damped
oscillations of astrophysical black holes, to greybody factors for the Hawking
radiation, and to more speculative state-counting models for the Bekenstein
entropy), to quantum field theory (where they are related to Casimir energies
in unbounded systems), through to condensed matter physics, (where one may
literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect
major additions and revisions. Now describes exact QNFs for the double-delta
potential in terms of the Lambert W function. V3: Minor edits for clarity.
Four references added. No physics changes. Still 31 page
Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
A quantum version of transition state theory based on a quantum normal form
(QNF) expansion about a saddle-centre-...-centre equilibrium point is
presented. A general algorithm is provided which allows one to explictly
compute QNF to any desired order. This leads to an efficient procedure to
compute quantum reaction rates and the associated Gamov-Siegert resonances. In
the classical limit the QNF reduces to the classical normal form which leads to
the recently developed phase space realisation of Wigner's transition state
theory. It is shown that the phase space structures that govern the classical
reaction d ynamicsform a skeleton for the quantum scattering and resonance
wavefunctions which can also be computed from the QNF. Several examples are
worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008)
R1-R11
Regularity of maximal operators: recent progress and some open problems
This is an expository paper on the regularity theory of maximal operators,
when these act on Sobolev and BV functions, with a special focus on some of the
current open problems in the topic. Overall, a list of fifteen research
problems is presented. It summarizes the contents of a talk delivered by the
author at the CIMPA 2017 Research School - Harmonic Analysis, Geometric Measure
Theory and Applications, in Buenos Aires, Argentina.Comment: 19 pages. Expository paper with the contents of a lecture given at
the in the CIMPA 2017 Research School - Harmonic Analysis, Geometric Measure
Theory and Applications, in Buenos Aires, Argentin
Deindustrialization in cities of the global south
Recent research by economists has shown that deindustrialization is more severe in Sub-Saharan Africa and Latin America than it ever was in the Organisation for Economic Co-operation and Development (OECD). Nevertheless, most research on deindustrialization is focused on the former centres of Fordist manufacturing in the industrial heartlands of the North Atlantic. In short, there is a mismatch between where deindustrialization is researched and where it is occurring, and the objective of this paper is to shift the geographical focus of research on deindustrialization to the Global South. Case studies from Argentina, India, Tanzania and Turkey demonstrate the variegated nature of deindustrialization beyond the North Atlantic. In the process, it is demonstrated that cities in the Global South can inform wider theoretical discussions on the impacts of deindustrialization at the urban scale
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