Hypersonic Flight Mechanics

The effects of aerodynamic forces on trajectories at orbital speeds are discussed in terms of atmospheric models. The assumptions for the model are spherical symmetry, nonrotating, and an exponential atmosphere. The equations of flight, and the performance in extra-atmospheric flight are discussed along with the return to the atmosphere, and the entry. Solutions of the exact equations using directly matched asymptotic expansions are presented

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations

Optimum three-dimensional atmospheric entry from the analytical solution of Chapman's exact equations

The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position

Analytic theory of orbit contraction

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory

CONTACT-INHIBITED REVERTANT CELL LINES ISOLATED FROM SV40-TRANSFORMED CELLS : IV. Microfilament Distribution and Cell Shape in Untransformed, Transformed, and Revertant Balb/c 3T3 Cells

A comparison is made of the ultrastructure of the cell periphery in three cloned cell lines: untransformed Balb/c 3T3 cells, SV40-transformed Balb/c 3T3 cells, and revertant cells obtained from the transformed cell line by a selection technique utilizing concanavalin A. Both thin-section and surface replication techniques are used for in situ examination of the cell lines. Microfilaments, 70 Å in diameter (called alpha filaments), are abundant in untransformed and revertant cell lines, particularly in the anterior expansions of the cells, which tend to have many microvilli and small pseudopodia. Alpha filaments are diminished in the anterior expansions of transformed cells, which contain large blunt pseudopodia and relatively few microvilli. Surface replicas confirm the impression gained from thin sections that transformed cells have a greater proportion of their cell surface involved in bulging pseudopodia than either untransformed or revertant cells. Since alpha filaments are shown to bind heavy meromyosin and are similar to F-actin, these filaments are thought to be important in cell motility. These observations suggest that a close relationship exists between decreased alpha filaments, bulging pseudopodia, and loss of contact inhibition of movement in transformed cells

Flight with lift modulation inside a planetary atmosphere

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76287/1/AIAA-7461-486.pd

Canine intrahepatic portosystemic shunt insertion into the systemic circulation is commonly through primary hepatic veins as assessed with CT angiography

Congenital intrahepatic portosystemic shunts (IHPSS) in dogs are traditionally classified as right, left, or central divisional. There are few descriptive studies regarding the variation of IHPSS within these categories. This multicenter, analytical, cross‐sectional study aimed to describe a large series of dogs with CT angiography (CTA) of IHPSS, hypothesizing that there would be variation to the existing classification. Ninety CTA studies were assessed for IHPSS type, insertion, and the relationship of the insertion to the primary hepatic veins. Ninety‐two percent of IHPSS inserted into a primary hepatic vein (HV) or phrenic vein, 8% inserted directly into the ventral aspect of the intrahepatic caudal vena cava. The most common IHPSS type was a single right divisional (44%), including those inserting via the right lateral HV or the caudate HV. Left divisional IHPSS (33%) inserted into the left HV or left phrenic vein. Central divisional IHPSS (13%) inserted into the quadrate HV, central HV, dorsal right medial HV, or directly into the ventral aspect of the intrahepatic caudal vena cava. Multiple sites of insertion were seen in 9% of dogs. Within left, central, and right divisional types, further subclassifications can therefore commonly be defined based on the hepatic veins with which the shunting vessel communicates. Relating IHPSS morphology to the receiving primary HV could make IHPSS categorization more consistent and may influence the type and method of IHPSS attenuation recommended