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Vinh, N. X.

Publications and source records attributed to Vinh, N. X..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Satellite dynamics about a planet with a narrow ring

The dynamics of a satellite attracted by a planet with a ring are investigated. A single model for the gravitational potential of a ring is used which extracts the fundamental gravitational effects on a satellite. Analytical and qualitative results are presented in cases where the satellites orbit is in the plane of the ring and where it is out of the plane of the ring. As final results we present equations expressing the perturbation of a body from two body motion when the ring is narrow. These effects include the advance of the argument of the periapsis and the precession of the plane of the orbit (when the satellite orbit is not contained in the ring plane). Additionally, inequalities on the angular momentum of the satellite (for the planar case) are found which guarantee that the orbits are bounded and do not intersect the ring.

Scheeres, D. J.↗
NASA NTRS1988

Chebyshev minimax problems for skip trajectories

The dimensionless equations of motion for hypersonic flight in the upper layer of the atmosphere are presented. The necessary conditions for the Chebyshev minimax problems are provided. Some important properties concerning the peak heating rate, the peak dynamic pressure and the peak altitude drop for a skip trajectory are discussed. As application of the theory, the problem of minimizing the peak altitude drop is solved. The numerical results support the theory that the nearly-grazing trajectory is useful in reducing the peak heating rate and the peak dynamic pressure.

Vinh, N. X.↗
NASA NTRS1988

Minimax optimal control for atmospheric fly-through trajectories

Necessary conditions for minimax problems with isolated or flat maxima are presented. Some relevant properties concerning the peak heating rate and the peak deceleration during atmospheric entry are discussed. As application of the theory, the problem of minimizing the peak heating rate of a skip trajectory is solved with special emphasis on the discussion of the continuity of the lift control at the point where the maximum occurs along the trajectory.

Lu, P.↗
NASA NTRS1988

Optimal plane change during constant altitude hypersonic flight

Future spacecraft operating in the vicinity of the earth may have resort to the atmosphere as an aid in effecting orbital change. While a previous treatment of this technique chose constant altitude, speed, and angle-of-attack values in order to maximize the plane change for a fixed amount of propellant consumption during hypersonic flight, the former two parameters are presently released from the constraint of constancy. The general characteristics of the optimal controls are described on the basis of the domain of maneuverability, and numerical solutions are obtained for several specific cases. Under the condition of constant-altitude flight, it is generally not optimal to fly at constant angle-of-attack.

Mease, K. D.↗
NASA NTRS1986

Necessary conditions for maximax problems with application to aeroglide of hypervelocity vehicles

This paper presents the necessary conditions for solving Chebyshev minimax (or maximax) problems with bounded control. The jump conditions obtained are applicable to problems with single or multiple maxima. By using Contensou domain of maneuverability, it is shown that when the maxima are isolated single points the control is generally continuous at the jump point in the minimax problems and discontinuous in the maximax problems in which the first time derivative of the maximax function contains the control variable. The theory is applied to the problem of maximizing the flight radius in a closed circuit glide of a hypervelocity vehicle and to a maximax optimal control problem in which the control appears explicitly with the first time derivative of the maximax function.

Vinh, N. X.↗
NASA NTRS1985

Optimal aeroassisted transfer between coplanar elliptical orbits

An attempt is made to solve the problem of orbital transfer between coplanar elliptical orbits. Pure propulsive transfer is analyzed with the restriction of two impulses for the transfer. The optimal switching conditions are reviewed, and it is shown that the solution is obtained by solving a set of three nonlinear equations for three unknowns. A semianalytical solution is obtained to the problem of planar rotation of an orbit for the pure propulsive maneuver, and it is shown that, for high eccentricity and rotation angle, aeroassisted transfer is a fuel-saving maneuver. It is demonstrated that complete circularization of the intermediate orbit is not necessary in the optimal aeroassisted transfer. An analytical proof is presented, giving an explicit condition for noncircularization. A complete numerical solution is presented for a case of optimal aeroassisted transfer from a low-energy orbit to a high-energy orbit.

Vinh, N. X.↗
NASA NTRS1985

Effect of maximum lift to drag ratio on optimal aeroassisted plane change

The influence of the maximum lift-to-drag ratio on the turning performance of an Orbital Transfer Vehicle is analyzed. Chapman's variables are used to formulate the equations of motion which are valid for both atmospheric flight and flight in a vacuum in a Newtonian gravitational field. Of the six adjoint variables involved in the variational formulation, four exact integrals and two approximate relations are obtained. This leads to an approximate but explicit control law for the lift and bank control. The control law is tested numerically for a whole range of entry speeds, from parabolic entry to near-circular entry with several values of maximum lift-to-drag ratio. The extensive numerical results, which are very accurate as compared to the exact optimal values, show that the maximum plane change for any speed ratio V(entry)/V(final) is simply proportional to the maximum lift-to-drag ratio, and depends solely on this parameter.

Johannesen, J. R.↗
NASA NTRS1984

Second-order analytic solution for aerocapture and ballistic fly-through trajectories

A generalized Yaroshevskii's system of equations is derived for analyzing ballistic entry at supercircular speeds. By an artificial introduction of a small parameter, the nonlinear system can then be integrated by Poincare's method. It is pointed out that the second-order theory displays explicitly the influence of the ballistic coefficient, entry speed, and entry angle on exit conditions. The analytic solution is found to be in excellent agreement with the numerical solution. Using an explicit formula, the critical entry angle at which the vehicle fails to skip out can be predicted to within one hundredth of a degree.

Vinh, N. X.↗
NASA NTRS1984

Explicit guidance of drag modulated aeroassisted transfer between elliptical orbits

This paper presents the complete analysis of the problem of minimum-fuel aeroassisted transfer between coplanar elliptical orbits in the case where the orientation of the final orbit is free for selection in the optimization process. The comparison between the optimal pure propulsive transfer and the idealized aeroassisted transfer, by several passages through the atmosphere, is made. In the case where aeroassisted transfer provides fuel saving, a practical scheme for its realization by one passage is proposed. The maneuver consists of three phases: a deorbit phase for nonzero entry angle, followed by an atmospheric fly-through with variable drag control and completed by a postatmospheric phase. An explicit guidance formula for drag control is derived and it is shown that the required exit speed for ascent to the final orbit can be obtained with a very high degree of accuracy.

Vinh, N. X.↗
NASA NTRS1983

Optimization and closed loop guidance of drag modulated aeroassisted orbital transfer

An analysis of optimal and near optimal atmospheric flight trajectories for drag modulated aeroassisted orbital transfer is presented. An explicit and adaptive closed loop guidance approach for this mode of orbit transfer is also presented with performance near the optimal nominal trajectories. The orbital transfer of interest is for return from high earth orbit to low earth orbit. Most of what is discussed in this paper concerns the aeroassisted or atmospheric segment which lowers the apogee of the high earth orbit to the apogee of the low earth orbit. Minimization of the total impulsive delta-V at this low earth orbit apogee is the optimization criterion. Control about this impulse due to a number of potential error sources in atmospheric braking is the requirement imposed on closed loop guidance.

Kechichian, J. A.↗
NASA NTRS1983

Optimal control of orbital transfer vehicles

During the past two decades, considerable research effort has been spent to convincingly prove that the use of aerodynamic forces to assist in the orbital transfer can significantly reduce the fuel consumption as compared to the pure propulsive mode. Since in this aeroassisted mode, preliminary maneuvers in the vacuum effect the resulting performance in the atmospheric phase, and vice versa, the two, space and atmospheric maneuvers, are, to a great extent, coupled. This paper summarizes, via optimal control theory, the fundamental results in the problem of orbital transfer using combined propulsive and aerodynamic forces. For the atmospheric phase, the use of Chapman's variables reduced the number of the physical characteristics of the vehicle and the atmosphere to a minimum and hence allows a better generalization of the results. The paper concludes with some illustrative examples.

Vinh, N. X.↗
NASA NTRS1983

Minimum-fuel aeroassisted coplanar orbit transfer using lift-modulation

Minimum-fuel trajectories and lift controls are computed for aeroassisted coplanar transfer from high orbit to low orbit. The optimal aeroassisted transfer requires less fuel than the all-propulsive Hohmann transfer for a wide range of high orbit to low orbit transfers. The optimal control program for the atmospheric portion of the transfer is to fly at maximum positive L/D initially to recover from the downward plunge, and then, to fly at negative L/D to level off the flight, such that the vehicle skips out of the atmosphere with a flight path angle near zero degrees. To avoid excessive heating rates, the vehicle flies initially at high angle of attack in order to slow down higher in the atmosphere, allowing recovery from the downward plunge, which occurs subsequently using the maximum positive L/D, to take place at a lower atmospheric density, or equivalently, at a higher altitude.

Mease, K. D.↗
NASA NTRS1982

Longitudinal control effectiveness and entry dynamics of a single-stage-to-orbit vehicle

The classical theory of flight dynamics for airplane longitudinal stability and control analysis was extended to the case of a hypervelocity reentry vehicle. This includes the elements inherent in supersonic and hypersonic flight such as the influence of the Mach number on aerodynamic characteristics, and the effect of the reaction control system and aerodynamic controls on the trim condition through a wide range of speed. Phugoid motion and angle of attack oscillation for typical cases of cruising flight, ballistic entry, and glide entry are investigated. In each case, closed form solutions for the variations in altitude, flight path angle, speed and angle of attack are obtained. The solutions explicitly display the influence of different regions design parameters and trajectory variables on the stability of the motion.

Vinh, N. X.↗
NASA NTRS1981

Phugoid oscillations in optimal reentry trajectories

A major problem with operations of lifting reentry vehicle having and aft center-of-gravity location due to large engine mass at the rear is the required hypersonic trim to fight the desired trajectory. This condition is most severe for lifting maneuvers. As a first step toward analyzing this problem, this paper considers the lift requirement for some basic maneuvers in the plane of a great circle. Considerations are given to optimal lift control for achieving the maximization of either the final altitude, speed or range. For the maximum-range problem, phugoid oscillation along an optimal trajectory is less severe as compared to a glide with maximum lift-to-drag ratio. An explicit formula for the number of oscillations for an entry from orbital speed is proposed.

Vinh, N. X.↗
NASA NTRS1981

Optimal trajectories in atmospheric flight

Aspects of optimization theory and switching theory are discussed, taking into account the necessary conditions for extrema, a solution subject to constraints, the calculus of variations, the Pontryagin maximum principle, the canonical transformation, Contensou's domain of maneuverability, optimal switching, a junction with singular arc, and linearized singular control. Equations of motion are considered along with aerodynamic and propulsive forces, the general properties of optimal trajectories, flight in a horizontal plane, optimal coasting flight, supersonic cruise, the supersonic turn, supersonic maneuvers in a vertical plane, energy state approximation, a modified Chapman's formulation for optimal reentry trajectories, optimal planar reentry trajectories, and an optimal glide of reentry vehicles. Orbital aerodynamic maneuvers are examined, giving attention to aerodynamic capture, a change in the apogee, a change in the eccentricity, a change in the perigee, an orbital maneuver, an aerodynamic maneuver, and a combined maneuver.

Vinh, N. X.↗
NASA NTRS1981

Optimal maneuvers at supersonic speeds in a vertical plane

This paper presents several optimal maneuvers of supersonic aircraft in a vertical plane. The general dimensionless equations of motion are derived and the computation of the optimal trajectories are carried out using the aerodynamics and engine characteristics of a light-weight fighter called the supercruiser. Because of the normalizing of the control variables, namely, the load factor and the thrust-to-weight ratio, the results applied to any supersonic aircraft. The optimality of the singular thrust control and the optimal junction of different subarcs are discussed. The proposed method of computing the optimal trajectory is very efficient and makes explicit the selection of the optimal control. The technique should be useful for performance assessment of supersonic aircraft with potential for implementation of onboard flight control system.

Vinh, N. X.↗