Engineering topics
Publications and source records attributed to Burns, J. A..
Cassini has identified a geologically active province a the south pole of Saturn's moon Enceladus. The shape of Enceladus suggests a possible intense heating epoch in the past by capture into a 1:4 secondary spin/orbit resonance.
Dust grains in planetary rings acquire stochastically fluctuating electric charges as they orbit through any corotating magnetospheric plasma. Here we investigate the nature of this stochastic charging and calculate its effect on the Lorentz resonance (LR). First we model grain charging as a Markov process, where the transition probabilities are identified as the ensemble-averaged charging fluxes due to plasma pickup and photoemission. We determine the distribution function P(t;N), giving the probability that a grain has N excess charges at time t. The autocorrelation function tau(sub q) for the strochastic charge process can be approximated by a Fokker-Planck treatment of the evolution equations for P(t; N). We calculate the mean square response to the stochastic fluctuations in the Lorentz force. We find that transport in phase space is very small compared to the resonant increase in amplitudes due to the mean charge, over the timescale that the oscillator is resonantly pumped up. Therefore the stochastic charge variations cannot break the resonant interaction; locally, the Lorentz resonance is a robust mechanism for the shaping of etheral dust ring systems. Slightly stronger bounds on plasma parameters are required when we consider the longer transit times between Lorentz resonances.
We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.
The dynamics of a weakly charged dust grain orbiting in the equatorial plane of a planet surrounded by a rigidly corotating magnetospehre is examined. It is shown that an introduction of an effectilve 1D potential causes a perturbation due to electrostatic forces, which induces a motion of the pericenter, similar to the effect of the planetary oblateness. A case is examined where the charge varies periodically due to the modulation of the photoelectron current occurring as the grain enters and leaves the planetary shadow, causing the electromagnetic perturbation to resonate with the orbital period and to modify the size and eccentricity of the orbit. This effect is demonstrated both numerically and analytically for small grains comprising the Jovian ring, showing that their resulting changes are periodic, and their amplitude is much larger than that of the periodic changes due to light-pressure perturbation or the secular changes due to resonant charge variations that develop over a comparable time span.
The particle properties and processes in the Uranian rings are analyzed from Voyager observations and ground-based data. Occultation observations of the epsilon ring are interpreted to yield an effective size of the ring particles that exceeds 70 cm, a surface mass density that exceeds 80 g/sq cm, and a ring vertical thickness greater than tens of meters for solid ice particles. The particles forming the classic rings are dark and gray, with albedo of 0.014 +/-0.004. It is argued that the small amount of dust that exists in the classical rings and between the rings in bands is created by erosion of ring particles and unseen satellites resulting from collisions and micrometeoroid bombardment. As proposed for regions of the other known ring systems, new ring material can be continually created by the destruction of small moons near the rings, which may explain the youthful appearance of the Uranian rings.
Well-posed models and computational algorithms are developed and analyzed for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. An abstract (state space) framework and a general well-posedness result are presented that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of a linear quadratic regulator (LQR) control problem. A detailed convergence proof is provided for the viscoelastic model and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.
The dynamics of small dust grains ejected from the Martian satellites is investigated, considering both the solar radiation perturbation and electromagnetic forces since the grains move in a magnetized plasma. Lorentz forces can dramatically change the nature of the trajectories, resulting in, for example, prolonged lifetimes for submicron-sized grains moving through an idealized model. It is suggested that a permanent, nonuniform and time-dependent dust halo of grains predominantly around 0.1 micron may exist about Mars.
The characteristics and distribution of the small particles detected by the plasma-wave and radio-astronomy instruments during the Voyager 2 encounter with Uranus in January 1986 are examined. The nature of the observational data and the analysis techniques employed are discussed, and the results are presented in graphs. Particles of rms mass about 2.6 ng and radii of a few microns were found in an impact region of thickness 3840 km, with a maximum number density of 1600/cu m about 280 km from the equatorial plane, shortly after Voyager 2 crossed the plane of the Uranian rings. The possible origin of the particles in the rings or in small satellites outside the rings is considered.
Finite dimensional approximation schemes that work well for distributed parameter systems are often not suitable for the analysis and implementation of feedback control systems. The relationship between approximation schemes for distributed parameter systems and their application to optimal control problems is discussed. A numerical example is given.
A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.
Enhancement of Voyager 2's parting shot of the Jupiter system reveals an additional ring. This ring is far fainter than either of the components previously identified, and extends to a radius of 210,000 km. The possible sources of this 'gossamer' ring are discussed.
Charged dust orbiting through spatially periodic planetary magnetic fields will experience time-variable electromagnetic forces. When the forcing frequencies are nearly commensurate with the particle's orbital frequency, the particle undergoes large out-of-plane and radial excursions. Specific 'Lorentz' resonances, corresponding to particular spatial periodicities in the magnetic field, occur on either side of synchronous orbit. Lorentz resonance locations and strengths for the Jovian and Saturnian rings are described. The boundaries of the halo of the Jovian ring, and perhaps other ring structures, are near resonances.
The structure of Jupiter's rings was studied in an effort to understand the processes that generate the rings. The faint material in the Saturn system was investigated leading to the discovery of a new ring and a way to interpret the wavy features surrounding Encke's division in terms of perturbing moonlets. The interaction of faint rings and magnetospheres helped identify some of the charged particle absorbers seen by Pioneer 11 in the neighborhood of the F ring. Angular momentum drain might account for the slow rotations of intermediate sized asteroids. Much of the Jovian ring structure can be understood in terms of debris loss from satellites, rapid orbital evolution, resonance, and charged dust dynamics.
The properties of planetary ring systems are summarized herein; emphasis is given to the available evidence on their compositions and to their dynamical attributes. Somewhat contaminated water ice makes up the vast expanse of Saturn's rings. Modified methane ice may comprise Uranus' rings while silicates are the likely material of the Jovian ring. Saturn's rings form an elaborate system whose characteristics are still being documented and whose nature is being unravelled following the Voyager flybys. Uranus' nine narrow bands display an intriguing dynamical structure thought to be caused by unseen shephard satellites. Jupiter's ring system is a mere wisp, probably derived as ejecta off hidden parent bodies.
Measurements of longitudinal variations in the brightness and in the latitude of the solar system dust bands recently discovered by IRAS will determine the orbital elements of the particles involved and may discriminate between cometary and asteroidal models of the origin of these bands. The expected variations for bands of dust particles with common orbital elements and small eccentricity and inclination are calculated as functions of semimajor axis.
It is shown that care must be taken to ensure that finite dimensional approximations of distributed parameter systems preserve important system properties (i.e., controllability, observability, stabilizability, detectability, etc.). It is noted that, if the particular scheme used to construct the finite dimensional model does not take into account these system properties, the model may not be suitable for control design and analysis. These ideas are illustrated by a simple example, i.e., a cable-spring-mass system.
It is shown that distinctive longitudinal variations in thermal flux and mean latitude can be used to determine the typical orbits of the grains comprising the Solar System bands. In particular, how the bands should vary if they are debris associated with the three principal asteroid families is predicted. Based on these ideas, IRAS observations may allow discrimination between asteroidal and cometary origins of the dust bands and, perhaps, of the entire zodiacal cloud.
The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.