Generalization of the Birkhoff Regularization of the Three Space Bodies Problem
Generalization of space restricted three-body problem by spinor regularization
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A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies
A three-dimensional virtual crack-closure technique is presented which calculates the strain energy release rates and the stress intensity factors using only nodal forces and displacements from a standard finite element analysis. The technique is an extension of the Rybicki-Kanninen (1977) method, and it assumes that any continuous function can be approximated by a finite number of straight line segments. Results obtained by the method for surface cracked plates with and without notches agree favorably with previous results.
Shivakumar, K. N.↗
Surface fitting three-dimensional bodies
The geometry of general three-dimensional bodies is generated from coordinates of points in several cross sections. Since these points may not be smooth, they are divided into segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction by fitting parametric cubic-spline curves through coordinate points which define the conic sections in the cross-sectional planes. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines and slopes at selected points. Slopes may be continuous or discontinuous and finite or infinite. After a satisfactory surface fit has been obtained, cards may be punched with the data necessary to form a geometry subroutine package for use in other computer programs. At any position on the body, coordinates, slopes and second partial derivatives are calculated. The method is applied to a blunted 70 deg delta wing, and it was found to generate the geometry very well.
Dejarnette, F. R.↗
Surface fitting three-dimensional bodies
The geometry of general three-dimensional bodies was generated from coordinates of points in several cross sections. Since these points may not be on smooth curves, they are divided into groups forming segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction through longitudinal curves. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines or specifying slopes at selected points. This method was used to surface fit a 70 deg slab delta wing and the HL-10 Lifting Body. The results for the delta wing were very close to the exact geometry. Although there is no exact solution for the lifting body, the surface fit generated a smooth surface with cross-sectional planes very close to prescribed coordinate points.
Dejarnette, F. R.↗
Topological classification of flow separation on three-dimensional bodies
In the study of three-dimensional, separated flows, a topological approach to separation and a phenomenological approach have been considered. The topological approach is based on ideas of Poincare (1928), while the phenomenological approach distinguishes between 'open' and 'closed' separation as posed by Wang (1974). In the present paper, the topological description provided by Legendre (1956, 1965, 1982) is considered, taking into account its utilization by Tobak and Peake (1979, 1982). An attempt is made to provide a more complete framework for the description of separated as well as attached flows. Nomenclature is introduced to describe the topology of the skin-friction-line portraits on a three-dimensional body. The topological ideas are illustrated by the use of hypothetical oil-flow experiments supplemented with actual flow-visualization data when possible.
Chapman, G. T.↗
Association reactions at low pressure. 5: The CH3(+)/HCN system. A final word?
The reaction of the methyl cation with hydrogen cyanide is revisited. We have confidence that we have resolved a long standing apparent contradiction of experimental results. A literature history is presented along with one new experiment and a re-examination of an old experiment. In this present work it is shown that all of the previous studies had made consistent observations. Yet, each of the previous studies failed to observe all of the information present. The methyl cation does react with HCN by radiative association, a fact which had been in doubt. The product ions formed in the two-body and three-body processes react differently with HCN. The collisionally stabilized association product formed by a three-body mechanism, does not react with HCN and is readily detected in the experiments. The radiatively stabilized association product, formed by a slow two-body reaction, is not detected because it reacts with HCN by a fast proton transfer reaction forming the protonated HCN ion. Previous studies either 'lost' this product in the extremely large protonated HCN signal that is always present when HCN is used, or discounted it for various reasons. We have been able to show by ion cyclotron resonance (ICR) techniques (both FT-ICR and tandem ICR-dempster-ICR) that the radiative association product does react with the HCN to form the protonated HCN ion.
Anicich, Vincent G.↗
Association Reactions at Low Pressure: 5. The CH(sub 3)+/HCN System. A Final Word?
The reaction of the methyl cation with hydrogen cyanide is revisited. We have confidence that we have resolved a long standing apparent contradiction of experimental results. A literature history is presented along with one new experiment and a reexamination of an old experiment. In this present work it is shown that all of the previous studies had made consistent observations. Yet, each of the previous studies failed to observe all of the information present. The methyl cation does react with HCN by radiative association, a fact which had been in doubt. The product ions formed in the two-body and three-body processes react differently with HCN. The collisionally stabilized association product formed by a three-body mechanism does not react with HCN and is readily detected in the experiments. The radiatively stabilized association product, formed by a slow two-body reaction, is not detected because it reacts with HCN by a fast proton transfer reaction forming the protonated HCN ion.
methyl cation↗
Defining an Abrasion Index for Lunar Surface Systems as a Function of Dust Interaction Modes and Variable Concentration Zones
Unexpected issues were encountered during the Apollo era of lunar exploration due to detrimental abrasion of materials upon exposure to the fine-grained, irregular shaped dust on the surface of the Moon. For critical design features involving contact with the lunar surface and for astronaut safety concerns, operational concepts and dust tolerance must be considered in the early phases of mission planning. To systematically define material selection criteria, dust interaction can be characterized by two-body or three-body abrasion testing, and subcategorically by physical interactions of compression, rolling, sliding and bending representing specific applications within the system. Two-body abrasion occurs when a single particle or asperity slides across a given surface removing or displacing material. Three-body abrasion occurs when multiple particles interact with a solid surface, or in between two surfaces, allowing the abrasives to freely rotate and interact with the material(s), leading to removal or displacement of mass. Different modes of interaction are described in this paper along with corresponding types of tests that can be utilized to evaluate each configuration. In addition to differential modes of abrasion, variable concentrations of dust in different zones can also be considered for a given system design and operational protocol. These zones include: (1) outside the habitat where extensive dust exposure occurs, (2) in a transitional zone such as an airlock or suitport, and (3) inside the habitat or spacesuit with a low particle count. These zones can be used to help define dust interaction frequencies, and corresponding risks to the systems and/or crew can be addressed by appropriate mitigation strategies. An abrasion index is introduced that includes the level of risk, R, the hardness of the mineralogy, H, the severity of the abrasion mode, S, and the frequency of particle interactions, F.
Kobrick, Ryan L.↗
Arrangement of fusiform bodies to reduce the wave drag at supersonic speeds
By means of linearized-body theory and reverse-flow theorems, the wave drag of a system of fusiform bodies at zero angle of attack and supersonic speeds is studied to determine the effect of varying the relative location of the component parts. The investigation is limited to two-body and three-body arrangements of Sears-Haack minimum-drag bodies. It is found that in certain arrangements the interference effects are beneficial, and may even result in the two or three-body system having no more wave drag than that of the principal body alone. The most favorable location appears to be one in which the maximum cross-section of the auxiliary body is slightly forward of the Mach cone from the tail of the main body. The least favorable is the region between the Mach cone from the nose and the forecone from the tail of the main body. (author)
Friedman, Morris D↗
Thresholds for the perception of angular acceleration about the three major body axes
Perception thresholds of rotation about three major body axes
Clark, B.↗
Arrangement of Bodies of Revolution in Supersonic Flow to Reduce Wave Drag
The wave drag of a combination of slender bodies of revolution at zero angle of attack is studied with a view to determining the arrangements for which the total drag is a minimum.Linearized theory is used to calculate the pressure distribution in the field surrounding the bodies. The interference drag coefficient is computed for different arrangements. The special cases of two bodies and of a three-body combination with bilateral symmetry are considered. The bodies treated are of the form determined by Sears and Haack as having minimum wave drag for prescribed volume and length. They also have equal fineness ratios. Numerical calculations of the drag coefficient of interference are carried out and curves are drawn which show the relative positions at which minimum drag occurs. A three-body configuration is found for which the total wave drag is about 35 percent less than the sum of the individual wave drags of the three bodies.
Friedman, Morris D↗
Radiation induced precursor flow field ahead of a reentering body.
Three dimensional flow field induced ahead of shock wave by radiation from shock layer over blunt body, determining perturbation velocity potential
Smith, G. L.↗
The topology of the regularized integral surfaces of the 3-body problem
Momentum, angular momentum, and energy of integral surfaces in the planar three-body problem are considered. The end points of orbits which cross an isolating block are identified. It is shown that this identification has a unique extension to an identification which pairs the end points of orbits entering the block and which end in a binary collision with the end points of orbits leaving the block and which come from a binary collision. The problem of regularization is that of showing that the identification of the end points of crossing orbits has a continuous, unique extension. The regularized phase space for the three-body problem was obtained, as were regularized integral surfaces for the problem on which the three-body equations of motion induce flows. Finally the topology of these surfaces is described.
Easton, R.↗
Metal-rich meteorites from the aubrite parent body
Three metal-rich meteorites - Mt. Egerton, Horse Creek, and LEW 88055 - were studied and it is suggested that they formed in the aubrite parent body. LEW 85369 and 88631 may also have a common origin, but these rocks have not yet been studied in detail. This body was probably heated to about 1600 C by a very strong heat source. While molten, metal agglomerated into sizeable nodules which never segregated efficiently to form a core, but were trapped in the silicate mantle. Different clasts and lithologies in aubrites solidified and cooled under local equilibrium conditions of oxygen fugacity, and with different thermal histories. Impacts mixed clasts from throughout the parent body, creating the typical aubrite breccias.
Casanova, I.↗
Calculation of trajectories using constant and slowly varying functions
A method is presented for calculating trajectories for the restricted problem of three bodies which utilizes conic propagation of the state vector with frequency correction of position and velocity by means of a constant or slowly varying function. This method of calculating trajectories was applied to the planar circular restricted three body problem, the planar elliptic restricted problem, and the ephemeral restricted problem. Two methods (the refined method and the straight forward method) of determining the direction of the position correction are presented for the circular restricted problem and the elliptic restricted problem of three bodies. Only the straight forward method was used with the ephemeral restricted problem. The earth, the moon, and a space vehicle comprise the restricted three body model that is used.
Culpepper, B. K.↗
An interactive method for surface fitting three-dimensional bodies
The paper discusses a computerized surface fitting procedure which, using interactive graphics, will surface fit mathematical relations to complex three-dimensional bodies. The program has been written so that it 'leads' the user step-by-step through the procedure, thus allowing a user of limited experience to rapidly digitize a body and obtain an accurate surface fit. Results are presented which indicate that the method yields accurate coordinates, slopes, and radii of curvature at any specified position on the body provided an adequate number of accurate cross section coordinates are available to adequately describe the body.
Perkins, J. N.↗
Lunar transfer trajectory design and the four-body problem
The existence of a ballistic trajectory from the Earth to orbit about the Moon was long considered to be impossible based on analysis of the three-body problem. In 1990 a ballistic trajectory from the Earth to lunar orbit was discovered while analyzing a plan to salvage the Muses A (Hiten) spacecraft. This trajectory utilized the Sun's gravity in conjunction with the Earth and Moon's gravity and was thus the first example of a practical four-body trajectory design. This paper presents a review of lunar transfer trajectories that go beyond three-body theory and the Jacobi integral. These include Hiten, Lunar A and the Genesis return trajectory from the vicinity of the Moon to Earth.It is shown that these trajectories may be analyzed by piecing together segments where three-body motion dominates.
Muses↗
Vertical Lift Planetary Aerial Vehicles: Three Planetary Bodies and Four Conceptual Design Cases
NASA Ames Research Center has been studying the feasibility of vertical lift aerial vehicles to support planetary science and exploration missions. Besides Earth, it appears that there are three planetary bodies within our solar system where vertical flight might not only be theoretically feasible, but would also have unique mission capabilities that no other platform (ground-based, aerial, or orbital) could provide. Several vertical lift vehicle configurations might be applicable for planetary science missions. This paper presents a few representative conceptual design cases and the design challenges inherent in their development. Finally, more detailed comments are directed to the issues inherent in developing a NASA Mars Scout mission employing the use of a Martian autonomous rotorcraft.
Young, Larry A.↗