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Trajectory computation technique for three-body motion is based on analytical derivation and empirical validation of pseudostate theory. Application of technique yields ''overlapped conic'' trajectories with error magnitudes only 20 percent as great as those of patched conic trajectories.
Membrane shell theory and digital computer program for determining impedance characteristics of thin conical shells under axial excitations
The theory and experimental work which demonstrated the feasibility of conical-scan tracking with a 64 m diameter paraboloid antenna is documented. The purpose of this scheme is to actively track spacecraft and radio sources continuously with an accuracy superior to that obtained by manual correction of the computer driven pointing. The conical-scan implementation gives increased tracking accuracy with X-band spacecraft signals, as demonstrated in the Mariner Venus/Mercury 1973 mission. Also, the high accuracy and ease of measurement with conical-scan tracking allow evaluation of systematic and random antenna tracking errors.
Stress and stability of thin-walled conical shells for axisymmetric loads
Thin conical shell under longitudinal impact, deriving theory for transverse and rotary inertias and transverse shear deformation effects
A model is presented that can account for several features of the dynamic spectral arcs observed at decameter wavelengths by the planetary radio astronomy experiment on Voyagers 1 and 2. It is shown that refraction of an extraordinary mode wave initially excited nearly orthogonal to the local magnetic field is significantly influenced by the local plasma density, being greater the higher the density. It is assumed that the source of the decameter radiation lies along the L = 6 flux tube and that the highest frequencies are produced at the lowest altitudes, where both the plasma density and magnetic field gradients are largest. It is further assumed that the decameter radiation is emitted into a thin conical sheet, consistent with both observation and theory. In the model the emission cone angle of the sheet is chosen to vary with frequency so that it is relatively small at both high and low frequencies, but approximately 80 deg at intermediate frequencies. The resulting emission pattern as seen by a distant observer is shown to resemble the observed arc pattern. The model is compared and contrasted with examples of Voyager radio data.
A rapid and accurate method of calculating optimal impulsive transfers in the restricted problem of three bodies has been developed. The technique combines a multi-conic method of trajectory integration with primer vector theory and an accelerated gradient method of trajectory optimization. A unique feature is that the state transition matrix and the primer vector are found analytical without additional integrations or differentiations. The method has been applied to the determination of optimal two and three impulse transfers between the L2 libration point and circular orbits about both the earth and the moon.
Force tests of a series of right circular cones having semivertex angles ranging from 5 deg to 45 deg and a series of right circular cone-cylinder configurations having semivertex angles ranging from 5 deg to 20 deg and an afterbody fineness ratio of 6 have been made in the Langley 11-inch hypersonic tunnel at a Mach number of 6.83, a Reynolds number of 0.24 x 10.6 per inch, and angles of attack up to 130 deg. An analysis of the results made use of the Newtonian and modified Newtonian theories and the exact theory. A comparison of the experimental data of both cone and cone-cylinder configurations with theoretical calculations shows that the Newtonian concept gives excellent predictions of trends of the force characteristics and the locations with respect to angle of attack of the points of maximum lift, maximum drag, and maximum lift-drag ratio. Both the Newtonian a.nd exact theories give excellent predictions of the sign and value of the initial lift-curve slope. The maximum lift coefficient for conical bodies is nearly constant at a value of 0.5 based on planform area for semivertex angles up to 30 deg. The maximum lift-drag ratio for conical bodies can be expected to be not greater than about 3.5, and this value might be expected only for slender cones having semivertex angles of less than 5 deg. The increments of angle of attack and lift coefficient between the maximum lift-drag ratio and the maximum lift coefficient for conical bodies decrease rapidly with increasing semivertex angles as predicted by the modified Newtonian theory.
Some of the background to contemporary jet aeroacoustics is addressed. Then scaling laws for noise generation by low-Mach-number airflows and by turbulence convected at 'not so low' Mach number is reviewed. These laws take into account the influence of Doppler effects associated with the convection of aeroacoustic sources. Next, a uniformly valid Doppler-effect approximation exhibits the transition, with increasing Mach number of convection, from compact-source radiation at low Mach numbers to a statistical assemblage of conical shock waves radiated by eddies convected at supersonic speed. In jets, for example, supersonic eddy convection is typically found for jet exit speeds exceeding twice the atmospheric speed of sound. The Lecture continues by describing a new dynamical theory of the nonlinear propagation of such statistically random assemblages of conical shock waves. It is shown, both by a general theoretical analysis and by an illustrative computational study, how their propagation is dominated by a characteristic 'bunching' process. That process associated with a tendency for shock waves that have already formed unions with other shock waves to acquire an increased proneness to form further unions - acts so as to enhance the high-frequency part of the spectrum of noise emission from jets at these high exit speeds.
A method is presented for calculating and optimizing unpowered planetary swingby trajectories using a patched conic trajectory generator. Examples of unpowered swingby trajectories are given to demonstrate the method. The method, which uses primer vector theory, is not highly accurate, but provides projections for preliminary mission definition studies. Advantages to using a patched conic trajectory simulation for preliminary studies which examine many different and complex missions include calculation speed and adaptability to changes or additions to the formulation.
Four pole parameters of truncated thin conical shell under axial excitations obtained by applying membrane shell theory
The pseudostate theory, which approximates three-body trajectories by overlapping the conic effects of both massive bodies on the third body, has been used to solve boundary value problems. Frequently, the approach to the secondary is quite close, as in interplanetary gravity assist trajectories or satellite tour trajectories. In this case the orbit with respect to the primary is radically changed so that perturbation techniques are time consuming, yet higher accuracy than point-to-point conics (V-infinity matching) is necessary. This method reduces the solution of the three-body Lambert problem to solving two conic Lambert problems and inverting a 7 x 7 matrix, the components of which are all found analytically. Typically 90-95% of the point-to-point conic error with respect to an integrated trajectory is eliminated.
The pseudostate theory, which approximates three-body trajectories by overlapping the conic effects of both massive bodies on the third body, has been used to solve boundary-value problems. Frequently, the approach to the secondary is quite close, as in interplanetary gravity-assist or satellite-tour trajectories. In this case, the orbit with respect to the primary is radically changed so that perturbation techniques are time consuming, yet higher accuracy than point-to-point conics is necessary. This method reduces the solution of the three-body Lambert problem to solving two conic Lambert problems and inverting a 7 x 7 matrix, the components of which are all found analytically. Typically 90-95 percent of the point-to-point conic error, with respect to an integrated trajectory, is eliminated.
Skin-temperature measurements have been made at several locations on a flat-faced cone-cylinder nose which was flight tested on a fivestage rocket-propeller model to a Mach number of 14.64 and a free-stream Reynolds number of 2.0 x 10(exp 6), based on flat-face diameter, at an altitude of 66,300 feet. The copper nose had a 29 deg total-angle conical section which was 1.6 flat-face diameters long. The aerodynamic-heating rates determined from the temperature measurements reached 1,440 Btu/( sec) (sq ft) on the flat face. The heating rates near the center of the flat face agreed well at Mach numbers up to 13.6 with those obtained by a theory for laminar stagnation-point heating in equilibrium dissociated air (Avco Res. Rep. 1). At Mach numbers above 13.6, the heating rates at locations near the center of the flat face became progressively lower than stagnation-point theory and. were 29 percent lower at Mach number 14.6 at the end. of the test. The reason for this behavior of the heating on the central part of the flat face was not determined. Excluding the relatively low heating rates that occurred on the central part of the nose at the highest Mach numbers, the distribution of experimental heating along the innermost 0.79 of the flat-face radius, expressed as a percentage of stagnation-point heating, was in fair agreement with the distribution predicted by laminar theory. At a location of 0.71 radii from the stagnation point, the experimental heating was very near 130 percent of the theoretical stagnation-point rate at Mach numbers from 11 to 14.5. The experimental beating rates on the conical section of the nose were in good agreement with laminar-cone theory using the assumption of theoretical sharp-cone static pressure on the conical section.
The geometry of spiral bevel gears and to their rational design are studied. The nonconjugate tooth surfaces of spiral bevel gears are, in theory, replaced (or approximated) by conjugated tooth surfaces. These surfaces can be generated by two conical surfaces, and by a conical surface and a revolution. Although these conjugated tooth surfaces are simpler than the actual ones, the determination of their principal curvatures and directions is still a complicated problem. Therefore, a new approach, to the solution of these is proposed. Direct relationships between the principal curvatures and directions of the tool surface and those of the generated gear surface are obtained. With the aid of these analytical tools, the Hertzian contact problem for conjugate tooth surfaces can be solved. These results are useful in determining compressive load capacity and surface fatigue life of spiral bevel gears. A general theory of kinematical errors exerted by manufacturing and assembly errors is developed. This theory is used to determine the analytical relationship between gear misalignments and kinematical errors. This is important to the study of noise and vibration in geared systems.
The heating of electron populations through resonant wave-particle interaction with upper hybrid turbulence is examined. It is first demonstrated that upper hybrid waves are easily excited by a population of warm electrons with a loss cone type distribution in a background of cold electron plasma. Quasi-linear theory is then used to show that the upper hybrid turbulence can preferentially heat the warm electrons in the perpendicular direction. In analogy to ion conic formation, this perpendicular heating process is a viable mechanism of generating electron conical distributions observed in the Earth's midaltitude polar regions.
An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.
It is found that under mild assumptions, feedback system stability can be concluded if one can 'topologically separate' the infinite-dimensional function space containing the system's dynamical input-output relations into two regions, one region containing the dynamical input-output relation of the 'feedforward' element of the system and the other region containing the dynamical output-input relation of the 'feedback' element. Nonlinear system stability criteria of both the input-output type and the state-space (Liapunov) type are interpreted in this context. The abstract generality and conceptual simplicity afforded by the topological separation perspective clarifies some of the basic issues underlying stability theory and serves to suggest improvements in existing stability criteria. A generalization of Zames' (1966) conic-relation stability criterion is proved, laying the foundation for improved multivariable generalizations of the frequency-domain circle stability criterion for nonlinear systems.