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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.
Analytical approach develops physical-mathematical model of rocket engine exhaust cloud rise, growth, and diffusion. Analytic derivations and resultant model apply to hot exhaust cloud study or industrial stack plumes, making work results applicable to air pollution. Model formulations apply to all exhaust cloud types and various atmospheric conditions.
A method is presented for calculating event probabilities from an arbitrary fault tree. The method includes an analytical derivation of the system equation and is not a simulation program. The method can handle systems that incorporate standby redundancy and it uses conditional probabilities for computing fault trees where the same basic failure appears in more than one fault path.
The results are presented of a study of the dynamics of a spinning Skylab space station. The stability of motion of several simplified models with flexible appendages was investigated. A digital simulation model that more accurately portrays the complex Skylab vehicle is described, and simulation results are compared with analytically derived results.
Experimental results of unlike doublet mixing are correlated with an analytically derived equation predicting fluid cavitation. The correlation relates the minimum orifice pressure drop required to initiate cavitation, with the system back pressure, cold flow simulant vapor pressure, and the orifice flow discharge and contraction coefficients. Stream flow instabilities are also visually correlated with the onset of cavitation and orifice discharge coefficient measurements. The influence of cavitation on the characteristic phenomenon of hydraulic flip is observed for both circular and noncircular shaped orifices. For certain intermediate orifice lengths, some noncircular shapes are shown to produce more fully developed flows (shorter recovery lengths) and therefore a more cohesive jet, which in turn yields slightly higher cold flow mixing uniformities than circular shaped orifices of equal absolute length. The particular noncircular shaped elements evaluated are shown to be more sensitive to liquid stream misimpingement than the corresponding circular orifices.
A simplified approximate expression is analytically derived for the spreading by charge exchange of a fine proton beam precipitating into the atmosphere. It shows in a simple way the dependence of proton beam spreading on atmospheric structure, collision data, primary particle energy, and pitch angle.
The distortion caused by a large-amplitude whistler (with wave normal parallel to the static magnetic field) on the energetic-electron velocity distribution of a predominantly cold magnetoplasma is derived analytically. Whistler test waves impressed on the perturbed magnetoplasma and within two narrow bands centered on the frequency of the original wave may experience large consecutive growth at the early stages of the wave-particle interaction if the unperturbed energetic-electron distribution satisfies two specified conditions. The relevance of these whistler side bands to magnetospheric phenomena is assessed; in particular, an identification of the onset of artificially stimulated emissions with the creation of whistler side bands gives good agreement with observations.
A new method to compute lunisolar perturbations in satellite motion is proposed. The disturbing function is expressed by the orbital elements of the satellite and the geocentric polar coordinates of the moon and the sun. The secular and long periodic perturbations are derived by numerical integrations, and the short periodic perturbations are derived analytically. The perturbations due to the tides can be included in the same way. In the Appendix, the motion of the orbital plane for a synchronous satellite is discussed; it is concluded that the inclination cannot stay below 7 deg.
A system of panoramic control densification is being developed to optimize production of lunar charts using Apollo 15 panoramic photography. It has been determined that such control developments may be combined with procedures for setting up stereo models for compilation on the AS-11 Analytical Stereoplotter. The procedure minimizes the number of analytically derived control points from metric photography required for model orientation and improves model-to-model fit for the compilation.
This paper presents the results of a study of the dynamics of a spinning Skylab space station. The stability of motion of several simplified models with flexible appendages was investigated. A digital simulation model that more accurately portrays the complex Skylab vehicle is described, and simulation results are compared with analytically derived results.
The flatness of the energy differential cross section in impact ionization is derived analytically in the Wannier theory. However it is shown that the Wannier zone is confined to a region of the order E/5 is less than or equal to epsilon is less than or equal to 4E/5, where E is the available energy and epsilon is the energy of the electrons. By contrasting the known results of photoionization and photodetachment, one can cogently argue that in the complementary region where electrons share their energy very unequally the cross section rises to a value independent of E, and that this region determines the form of the threshold law.
A simple second-order digital phase-locked loop has been designed to synchronize itself to a square-wave subcarrier. Analysis and experimental performance are given for both acquisition behavior and steady-state phase error performance. In addition, the damping factor and the noise bandwidth are derived analytically. Although all the data are given for the square-wave subcarrier case, the results are applicable to arbitrary subcarriers that are odd symmetric about their transition region.
A pulse-limited split-gate-tracking radar altimeter was flown on Skylab and will be used aboard GEOS-C. If such an altimeter were to employ a hypothetical isotropic antenna, the altimeter output would be independent of spacecraft orientation. To reduce power requirements the gain of the altimeter antenna proposed is increased to the point where its beamwidth is only a few degrees. The gain of the antenna consequently varies somewhat over the pulse-limited illuminated region of the ocean below the altimeter, and the altimeter output varies with antenna orientation. The error introduced into the altimeter data is modeled empirically, but close agreements with the expected errors was not realized. The attitude error effects expected with the GEOS-C altimeter are modelled using a form suggested by an analytical derivation. The treatment is restricted to the case of a relatively smooth sea, where the height of the ocean waves are small relative to the spatial length (pulse duration times speed of light) of the transmitted pulse.
A quadratic extended interior penalty function formulation especially well suited for second-order unconstrained optimization procedures is presented. Analytical derivatives of constraints and an approximate analysis technique are used. Minimum-mass design results are presented which indicate that the combination of these procedures can help make mathematical programming a useful optimization tool for large-order structural design problems with a large number of design variables and multiple constraints. Examples include statically loaded high- and low-aspect-ratio wings simultaneously subjected to stress, displacement, minimum gage and, in some cases, maximum strain constraints.
The assumption of factorized Green's functions together with the inhomogeneous Teukolsky equations are used to derive analytic expressions for homogeneous metric (and vector potential) perturbations of a Kerr black hole. These homogeneous solutions are used to construct solutions to the perturbation equations when sources are present. What one finds are particularly simple formulas for the energy and angular momentum flux in the asymptotic regions at plus or minus infinity.-
On present day high performance aircraft, a large portion of the lift is generated by leading edge vortices generated by flow separation off the highly swept leading edges of the lifting surfaces employed. It has been shown in an earlier paper how the vortex effects can be superimposed on a modified slender wing theory to give the unsteady longitudinal characteristics of sharp-edged delta wings up to very high angles of attack. The present paper extends the previous analysis to include the effects of leading edge roundness and trailing edge sweep on the aerodynamic characteristics. The paper also derives analytic means for prediction of the yaw stability of slender wings and the first order effects of Mach number. Universal scaling laws are defined for rapid preliminary design estimates of the slender wing lift and rolling moment. The results indicate that simple analytic tools can be developed to predict the aeroelastic characteristics of the space shuttle ascent configuration with its complicated flow field and aeroelastic cross-couplings.
Drum-peel tests are made more meaningful by use of approximations to derive analytical expressions relating failures due to bond flatwise tension, inplane tension, and shear, to adhesive weight and method of bond cure.
An analytically derived approach to the control of energy-storage dc-to-dc converters, which enables improved system performance and an extensive understanding of the manner in which this improved performance is accomplished, is presented. The control approach is derived from a state-plane analysis of dc-to-dc converter power stages which enables a graphical visualization of the movement of the system state during both steady state and transient operation. This graphical representation of the behavior of dc-to-dc converter systems yields considerable qualitative insight into the cause and effect relationships which exist between various commonly used converter control functions and the system performance which results from them.