In this paper, a new guidance problem with the impact time constraint is investigated, which can be applied to salvo attack of anti-ship missiles. The closed form solution based on the linear formulation is derived, suggesting an additional loop for adjusting the impact time in addition to the traditional optimal guidance loop. This solution is a combination of the well-known PNG law and the feedback of the impact time error, which is the difference between the impact time by PNG and the prescribed impact time. The new guidance law called ITCG (Impact-Time-Control Guidance) can be used to guide multiple missiles to hit a stationary target simultaneously at a desirable impact time. Nonlinear simulation of several engagement situations demonstrates the performance and feasibility of ITCG. In addition, the similarity of the closed form solution and APNG is investigated and the switching rule for practical implementation is discussed.

Impact-time-control guidance law for anti-ship missiles

A methodology for very fast design of three-degree-of-freedom (3DOF) entry trajectories subject to all common inequality and equality constraints is developed. The approach makes novel use of the quasi-equilibrium glide phenomenon in lifting entry as a centerpiece for effective and efficient enforcement of the inequality constraints. The highly constrained nonlinear trajectory planning problem is decomposed into two sequential one-parameter search problems. The algorithm is able to generate a complete and feasible 3DOF entry trajectory of 25-min flight time in about 2-3 s on a desktop computer, given the entry conditions, values of constraint parameters, and final conditions. High-fidelity numerical simulations with a reusable launch vehicle model for various entry missions and trajectory planning using the space shuttle model are presented to demonstrate the capability and effectiveness of the algorithm.

Onboard Generation of Three-Dimensional Constrained Entry Trajectories

Confluent Hypergeometric Functions.

Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey

Introduction I N 1961, Howard London presented a paper at the 29th Annual Meeting of the Institute of the Aeronautical Sciences in which he demonstated the possibility of using aerodynamic forces to produce an orbital plane change with an expenditure of energy significantly smaller than that associated with an extra-atmospheric propulsive maneuver. Since that time, numerous studies of aeroassisted orbit transfer have been carried out for a wide variety of Earthorbital and planetary missions. Almost any mission that involves changes in orbital altitude and/or inclination in the vicinity of an atmosphere-bearing planet is a candidate for aeroassist. For ease of discussion these many possible mission applications may be categorized as 1) synergetic plane change, 2) planetary mission applications, and 3) orbital transfer vehicle applications. The term, synergetic plane change, is commonly used to denote a maneuver in which a change in orbit inclination is accomplished through a combination of aerodynamic and propulsive forces rather than through propulsion alone. While the maneuver is applicable to any planet with a suitable atmosphere, practically all studies to date have dealt with low Earth orbit missions. As illustrated in Fig. 1, a retrorocket burn causes the vehicle to leave its initial low Earth orbit (LEO) and dip into the atmosphere. During the atmospheric pass, the vehicle is banked so that the lift vector is in a lateral direction, thus producing an aerodynamic turn. As will be discussed subsequently, this turn is often accomplished with continuous thrusting sufficient to balance the aerodynamic drag. Following the aerodynamic turn, the vehicle is reboosted to the desired orbital altitude and a rocket burn is effected to circularize the orbit (shown by the dashed low Earth orbit in Fig. 1). The typical orbital transfer vehicle (OTV) maneuver is in many ways similar to the synergetic plane change. In the OTV case, however, the vehicle is initially in a high Earth orbit (HEO)—geosynchronous in most studies—and must undergo a sizeable velocity decrement in its transfer to LEO as illustrated in Fig. 1. This velocity decrement is more efficiently achieved through a combination of aerodynamic drag and propulsion than through propulsion alone. The OTV mission usually involves some change in orbital plane—for instance, the return from geosynchronous orbit to a typical Shuttle orbit involves a plane change of 28.5 deg. If the OTV is a lifting configuration, some of the required plane change can be achieved by banking the vehicle as in the synergetic plane change maneuver. In planetary mission applications, aeroassist is again used to produce a velocity decrement through aerodynamic drag. For these missions two distinctly different applications of aeroassist have been studied: 1) aerocapture in which the velocity decrement achieved in a single deep atmospheric pass is sufficient to transfer the vehicle from its hyperbolic approach trajectory to a target orbit about the planet (i.e., the vehicle is captured by the planet's gravitational field); and 2) multipass aerobraking in which the vehicle is transferred from its approach trajectory to a highly elliptic orbit about the planet by a rocket burn and then the orbit is circularized by many high-altitude atmospheric passes, each followed by small corrective rocket burns at apoapsis to maintain the periapsis altitude low enough to produce the desired drag decrement but high enough to avoid excessive aerodynamic heating. The first type of planetary application, as illustrated in Fig. 1, is similar to the OTV maneuver except that it usually has a larger velocity excess and no plane change. The second type of planetary application is illustrated in Fig. 2. As is also illustrated in Fig. 2, this type of multipass orbit lowering has also been studied for the GEO-to-LEO OTV mission. In the intervening years since London presented his paper in 1961, many studies have been carried out and a rich literature has developed. In the process of researching the present paper, an extensive bibliography was compiled. It lists the relevant publications in chronological order for each of the three vehicle classes considered. While certainly incomplete (new and additional references keep turning up), this collection of papers is believed to present an accurate overall picture of the evolution of aeroassist technology. Examination of this bibliography shows that the various aeroassist mission applications received their most intensive study in different time periods. As was mentioned previously, the serious study of synergetic plane change maneuvers began with London's paper in 1961. Actually, there were studies published prior to 1961 (e.g., Ref. 1) but London's paper appears to be the first to convincingly demonstrate a significant performance gain. During the 1960s, synergetic plane change was studied extensively with the peak activity occurring around 1967. The initial

A Survey of Aeroassisted Orbit Transfer

The book treats hypersonic flight trajectories and atmospheric entry flight mechanics in light of their importance for space shuttle entry Following a review of the structures of planetary atmospheres and aerodynamic forces, equations are derived for flight over a spherical planet, and the performance of long-range hypervelocity vehicles in extra-atmospheric flight is analyzed Consideration is then given to vehicle trajectories in the powered and atmospheric reentry phases of flight, and several first-order solutions are derived for various planetary entry situations The second-order theory of Loh for entry trajectories is presented along with the classical theories of Yaroshevskii and Chapman for entry into planetary atmospheres, and the thermal problems encountered in hypersonic flight are analyzed A unified theory for entry into planetary atmospheres is then introduced which allows the performance of a general type of lifting vehicle to be studied, and applied to the analysis of orbit contraction due to atmospheric drag, flight with lift modulation and lateral maneuvers

Hypersonic and planetary entry flight mechanics

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.

Optimal trajectories in atmospheric flight

Preface Introduction Equations of motion Aerodynamic forces Propulsion systems Descent and glide performance Cruise performance Climb performance Turning performance Turning flight of jet aircraft Take-off and landing performance Performance of hypervelocity re-entry vehicles Appendices Selected bibliography Index.

Flight Mechanics of High-Performance Aircraft

Acontrol lawisderivedandanalyzed thatstabilizesa classof unstableperiodicorbitsin theHillrestrictedthreebody problem. The control law is derived by stabilizing the short-time dynamics of motion about a trajectory by the use of a feedback law specie ed by the instantaneous eigenvalue and eigenvector structure of the trajectory. This law naturally generalizes to a continuous control law along an orbit. By applying the control to an unstable periodic orbit, we can explicitly compute the stability of the control over long periods of time by computing the monodromy matrix of the periodic orbit with its neighborhood modie ed via the control law. For the case of an unstable halo periodic orbit in the Hill restricted three-body problem, we e nd that the entire periodic orbit can be stabilized. The resulting stable periodic orbits have three distinct oscillation modes in their center manifold. We discuss how this control can be applied to formation e ight about a halo orbit. Some practical implementation issues of the control are also considered. We show that the control acceleration can be provided by a low-thrust engine and that the total fuel cost of the control can be quite reasonable. I. Introduction T HIS paper studies the stabilization of an unstable periodic orbit in the Hill problem, which can serve as a general model for motion in the Earth‐ sun system. Results of this study will be relevant to the dynamics and control of a constellation of spacecraft in an unstable orbitalenvironment such as found near the Earth‐ sun libration points. It will also shed light on the practical control and computation of a single spacecraft trajectory in an unstable orbital environment over long time spans. We investigate the application of feedback control laws to stabilize a periodic orbit in the sense of Lyapunov (see Ref. 1) (note, not asymptotic stability). Thus, the stabilized trajectory will consist of oscillatory motions about the nominal trajectory, which in this context can be interpreted as motions in the center manifold of the stabilized periodic orbit. We show that an entire class of such control laws can be dee ned and their stability analyzed as a timeperiodic linear system. The fuel expenditure for such control laws is often quite small and scales with the mean distance between the controlled motion and the nominal trajectory (which is a periodic orbit in this application). The problem of spacecraft control in unstable orbits is not new. (See Refs. 2 and 3 for reviews.) However, these previous studies have focused on stationkeeping control for a single spacecraft and have not considered how the relative motion of a formation of spacecraft could be stabilized and their dynamics modie ed, which is what we consider here. Proposed space observatories of the future include ambitious interferometricimagersthatusebaselinesofhundredsorthousandsof kilometers between spacecraft to attain sufe ciently high resolutions to image planets around distant stars. To carry out these imaging procedures requires that the relative motion between spacecraft be known extremely accurately and that the spacecraft “ e ll in” an effective image e eld as they move relative to each other. A periodic

Nguyen X. Vinh

Papers

Hypersonic and planetary entry flight mechanics

Optimal trajectories in atmospheric flight

Optimal trajectories in atmospheric flight

Flight Mechanics of High-Performance Aircraft

Stabilizing Motion Relative to an Unstable Orbit: Applications to Spacecraft Formation Flight