Engineering topics
Publications and source records attributed to Burns, J. A..
A numerical procedure is proposed for solving optimal control problems governed by linear retarded functional differential equations. The procedure is based on the idea of 'averaging approximations', due to Banks and Burns (1975). For illustration, numerical results generated on an IBM 370/158 computer, which demonstrate the rapid convergence of the method are presented.
The paper deals with methods of obtaining approximate solutions to linear retarded functional differential equations (hereditary systems). The basic notion is to project the infinite dimensional space of initial functions for the hereditary system onto a finite dimensional subspace. Within this framework, two particular schemes are discussed. The first uses well-known piecewise constant approximations, while the second is a new method based on piecewise linear approximating functions. Numerical results are given.
The orbital evolution of a large satellite is governed primarily by tidal interactions between the satellite and the planet it orbits. Tides raised on a planet by a satellite transfer energy and angular momentum to the satellite orbit; this changes the semimajor axes of satellite orbits, increasing the size of those orbits where the satellite mean motion is smaller than the planetary angular velocity, and decreasing those where the opposite is true. Substantial changes caused by such tides for satellites of the terrestrial planets may explain the absence of satellites about Mercury and Venus. For Jovian and Saturnian satellites, such tides probably are only important in bringing about some of the observed orbital resonances. Tides raised on satellites generally cause decreasing orbital eccentricities, indicating why close satellites always have nearly circular orbits. Different processes of orbital evolution dominate for small bodies; their effects probably are critical in positioning material in the primordial dust cloud so that satellite coagulation may occur. A qualitative description is given of the orbital results of gas drag, radiation pressure, Poynting-Robertson drag and electromagnetic forces.
Information about Mercury obtained with the Mariner 10 spacecraft is summarized together with results of theoretical studies and ground-based observations. It is shown that Mercury is very likely a differentiated body, probably contains a large earthlike iron-rich core, and displays a surface similar to the moon's, which suggests a similar evolutionary history. The size and mass of Mercury are discussed along with its orbit, rotation, atmosphere, magnetic field, and magnetosphere. Surface features of Mercury are described on the basis of Mariner 10 pictures, with detailed attention given to the major physiographic provinces, the structure of the Caloris basin, the tectonic framework of the planet, crater morphology, the planet's optical and thermal properties, and cartography. The composition and structure of the interior are examined, and the thermal history of Mercury is considered. The planet's geologic history is divided into five stages or epochs: (1) accretion and differentiation, (2) terminal heavy bombardment, (3) Caloris basin formation, (4) basin flooding, and (5) postfilling lighter bombardment.
Robertson's expression for the velocity-dependent effect of solar radiation on the motion of small particles is difficult because of its dependence on relativistic considerations, and it is also deficient in that it assumes perfectly absorbing particles. The present paper gives a heuristic derivation of the Poynting-Robertson effect. Robertson's expression for perfectly absorbing particles is obtained but on a much simpler physical basis, and an expression is also obtained for a particle that in general scatters, transmits, and absorbs light. Some numerical results on the solar radiation forces felt by small particles of cosmochemically important compositions are given.
An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.
Prior to the flight of the Mariner 10 spacecraft, Mercury was the least investigated and most poorly known terrestrial planet (Kuiper 1970, Devine 1972). Observational difficulties caused by its proximity to the Sun as viewed from Earth caused the planet to remain a small, vague disk exhibiting little surface contrast or details, an object for which only three major facts were known: 1. its bulk density is similar to that of Venus and Earth, much greater than that of Mars and the Moon; 2. its surface reflects electromagnetic radiation at all wavelengths in the same manner as the Moon (taking into account differences in their solar distances); and 3. its rotation period is in 2/3 resonance with its orbital period. Images obtained during the flyby by Mariner 10 on 29 March 1974 (and the two subsequent flybys on 21 September 1974 and 16 March 1975) revealed Mercury's surface in detail equivalent to that available for the Moon during the early 1960's from Earth-based telescopic views. Additionally, however, information was obtained on the planet's mass and size, atmospheric composition and density, charged-particle environment, and infrared thermal radiation from the surface, and most significantly of all, the existence of a planetary magnetic field that is probably intrinsic to Mercury was established. In the following, this new information is summarized together with results from theoretical studies and ground-based observations. In the quantum jumps of knowledge that have been characteristic of "space-age" exploration, the previously obscure body of Mercury has suddenly come into sharp focus. It is very likely a differentiated body, probably contains a large Earth-like iron-rich core, and displays a surface remarkably similar to that of the Moon, which suggests a similar evolutionary history.
The equations of celestial mechanics that govern the temporal rates of change of orbital elements are completely derived using elementary dynamics and proceeding only from Newton's equation and its solution. Two orbital equations and the four most meaningful orbital elements - semimajor axis, eccentricity, inclination, and longitude of pericenter - are written in terms of the orbital energy (E) and angular momentum (H) per unit mass. The six resulting equations are differentiated with respect to time to see the effect on the orbital elements of small changes in E and H. The usual perturbation equations in terms of disturbing-force components are then derived by computing the manner in which perturbing forces change E and H. The results are applied in a qualitative discussion of the orbital evolution of particles in nonspherical gravitational fields, through atmospheres, and under the action of tides.
The papers consider the orbits, physical properties, composition, origin, and evolution of the natural satellites of the solar system from the viewpoint of celestial mechanics. Topics include a computer technique for developing analytic expressions for the coordinates and partial derivatives of Jupiter's Galilean satellites, a theory of the motion of the Galilean satellites, a comparison between photographic observations of the positions of the Galilean satellites and Sampson's tables, astrolabe observations of several transits of the Galilean satellites, the orbital resonance among the Galilean satellites, the motion of the Martian satellites from ground-based observations and Mariner-9 TV data, and a general method for predicting eclipses of natural planetary satellites. Individual items are announced in this issue.
Six-color photometric observations made during Saturn's 1972/73 opposition enable us to separate the solar phase and orbital phase contributions to the observed light variations of Iapetus, Titan, Rhea, Dione and Tethys. Titan shows no orbital variations, but has phase coefficients which range from negligible values in the infrared to 0.014 mag/deg in the ultraviolet. Rhea has a bright leading side, a light curve amplitude of about 0.2 mag, and surprisingly large phase coefficients. Combined with other available information, the observations suggest a very porous, texturally complex surface layer. Dione has a leading side which is a few tenths of a magnitude brighter than the trailing side, but the light curve amplitude has little wavelength dependence and the phase coefficients are significantly smaller than those of Rhea, suggesting a less intricate surface texture. The leading side of Tethys is probably a few tenths of a magnitude brighter than the trailing side. Our Iapetus observations generally supplement the earlier work by Millis.
The extensive photometric observations of Titan, Iapetus, Rhea, Dione and Tethys have made it possible to separate the solar phase and orbital phase contributions to the observed light variations of these satellites. For Titan, the wavelength dependence of its solar phase coefficient has been obtained. This dependence should prove useful in constructing future model atmospheres. The other four satellites show a surprising array of different photometric behaviors. Despite these differences, all four satellites have similar spectral reflectivities. Clearly Iapetus, Rhea, Dione and Tethys are complex objects, varying substantially from one another in surface structure and/or composition.
The orbital properties of the two small Martian satellites, Phobos and Deimos, are discussed, as well as those dynamical constants of Mars that can be determined from the satellite orbits. The secular acceleration of the mean motion of Phobos is shown to be very small. Of mechanisms that could cause any such acceleration, only tidal friction appears to be important. From the orbital evolution of the Martian satellites under tidal forces, Phobos and Deimos seem to have originated in nearly circular orbits of low inclination fairly close to the distance at which a satellite's orbital period is the planet's rotation period. It is proposed that the Martian satellites were born at the same time as Mars from equatorial dust clouds. The satellites are predicted to be locked in synchronous rotation, with their axes of minimum moment of inertia pointing on the average toward Mars, whereas their maximum axes are approximately normal to their orbit planes.
Charged particle dynamics in spiral interplanetary magnetic field model, discussing electric drift velocity, point of origin and distribution
Solar wind mechanism for origin of planetary rotation, discussing previous calculations of angular velocity and couple acting on planet
Drift rates and adiabatic guiding center motion of charged particle in idealized interplanetary magnetic fields
Jupiter decametric radiation properties explained by postulating inner Galilean satellite magnetic field existence