Showing papers by "University of Colorado Colorado Springs published in 1969"

Optimum maneuvers of a skip vehicle with bounded lift constraints.

Abstract: This paper presents the analytical solutions of the problem of optimum maneuvering of a glide vehicle flying in the hypervelocity regime. The investigation is based on the approximation of Allen and Eggers; namely, that along the fundamental part of a reentry or ascent trajectory, the aerodynamic forces greatly exceed the components of the gravitational force in the directions tangent and normal to the flight path. The problem consists of finding an optimal control law for the lift such that the final velocity or the final altitude is maximized. This problem can be viewed as bringing the vehicle to the best condition for interception, penetration, or making an evasive maneuver. If the range is free, the optimal lift control is obtained in closed form. If the lift control is bounded, then bounded control is optimal whenever it is reached. The switching sequences for different cases are discussed, and it is shown that there are at most two switchings. Bounded lift control is always at the ends of the optimal trajectory; for the case of two switchings, the optimal trajectory has an inflection point.

An analytical technique for studying the anomalous roll behavior of re-entry vehicles

Abstract: Anomalous roll behavior of a spinning re-entry vehicle is examined in detail for the case of a vehicle having a simple compound asymmetry consisting of a lateral center-of-gravity offset combined with an aerodynamic trim angle of attack. The analysis is made utilizing a fast analytical roll response program developed from the linearized equations of motion of a spinning vehicle. The results show that persistent roll resonance is obtained at first resonance with the minimum aerodynamic asymmetry if the asymmetry creates a trim force that lies in-plane with the center-of-gravity offset. A criterion is developed which defines this minimum in-plane aerodynamic asymmetry for the special case of a constant flightpath entry into an exponential atmosphere with constant aerodynamic coefficients. A suggested method of treating Mach-number-dependent aerodynamic coefficients is also presented. Selected six-degree-of-freedom trajectory calculations are used to verify important analytical results.

Screening Constants and Transition Energies

Abstract: Atomic screening constants usually are derived by minimizing ground‐state energies or by comparing known system energies with those calculated with simple wavefunctions containing screening constants. One set was derived, however, by matching moments of simple wavefunctions containing screening constants to moments of Hartree–Fock wavefunctions. These screening constants represent the individual interactions of a given electron with each of the other electrons of the system. They are, therefore, particularly useful for calculating bound–bound and bound–free transition energies in ions. Neutral atom electron binding energies calculated using these screening constants disagreed with published best values. We adjusted the screening constants empirically to reproduce closely these best values of binding energies. Using the adjusted screening constants, we calculated K‐ and L‐shell transition energies in neutral atoms and ions and obtained good agreement with accepted values.

Computer-aided design of the flood beam system for a direct view storage CRT

Abstract: The flood beam in a direct view storage CRT must uniformly illuminate the storage surface. Variable persistence operation of the CRT also requires that the electron trajectory at the storage surface be within about 5 degrees from perpendicular. Thus, an initially diverging beam must be collimated near the screen.

An analytical technique for studying the anomalous roll behavior of re-entry vehicles

Abstract: Anomalous roll behavior of a spinning re-entry vehicle is examined in detail for the case of a vehicle having a simple compound asymmetry consisting of a lateral center-of-gravity offset combined with an aerodynamic trim angle of attack. The analysis is made utilizing a fast analytical roll response program developed from the linearized equations of motion of a spinning vehicle. The results show that persistent roll resonance is obtained at first resonance with the minimum aerodynamic asymmetry if the asymmetry creates a trim force that lies in-plane with the center-of-gravity offset. A criterion is developed which defines this minimum in-plane aerodynamic asymmetry for the special case of a constant flightpath entry into an exponential atmosphere with constant aerodynamic coefficients. A suggested method of treating Mach-number-dependent aerodynamic coefficients is also presented. Selected six-degree-of-freedom trajectory calculations are used to verify important analytical results.