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In this paper, a numerical method is proposed for determining the periodic state and control solutions of nonlinear time-periodic systems. Starting from an initial guess at the solution, the algori...

This paper studies the flight dynamics and control strategy for electric solar wind sails based on the nodal position finite element method, where the coupling effects between tether dynamics and t...

As part of the upcoming Mars 2020 rover mission, NASA is planning to include an autonomous helicopter to demonstrate the feasibility and utility of using helicopters for Mars exploration. Helicopte...

The advent of fly-by-wire technology brought many advantages to aircraft design, but also increased the number of occurrences of the undesirable pilot-induced oscillation phenomena. To analyze such...

This paper presents an integrated flight control system with rotor-state feedback for helicopter approaching to the ship deck. First, a high-order nonlinear flight dynamics model coupled with the r...

A time-varying model for the forward flight dynamics of a flapping-wing micro aerial vehicle is identified from free-flight optical tracking data. The model is validated and used to assess the validity of the widely applied time-scale separation assumption. Based on this assumption, each aerodynamic force and moment is formulated as a linear addition of decoupled time-averaged and time-varying submodels. The resulting aerodynamic models are incorporated in a set of linearized equations of motion, yielding a simulation-capable full dynamic model. The time-averaged component includes both the longitudinal and the lateral aerodynamics and is assumed to be linear. The time-varying component is modeled as a third-order Fourier series, which approximates the flapping dynamics effectively. Combining both components yields a more complete and realistic simulation. Results suggest that while in steady flight the time-scale separation assumption applies well during maneuvers the time-varying dynamics are not fully captured. More accurate modeling of flapping-wing flight during maneuvers may require considering coupling between the time scales.

Time delays arise in most feedback systems and have specific relevance for remotely piloted vehicles with ground-based pilots and controllers. NASA’s test facility for flight dynamics and control research using subscale vehicles, the Airborne Subscale Transport Aircraft Research facility, has developed the remotely piloted generic transport model. Analysis of a numerical model of this has previously provided insight into open-loop upset dynamics and the impact of flight controllers. However, to date, studies have not considered the effect of time delay on the system’s stability. Current developments at the Airborne Subscale Transport Aircraft Research facility are aimed at testing a subscale generic airliner model during loss-of-control conditions over extended distances and altitudes compared to the generic transport model. In developing controllers for such a remotely piloted vehicle, it is helpful to understand the effect of delay in the communication links and protocols. This paper uses bifurcation an...

This paper describes the development of a methodology to assess the handling qualities requirements for vertical takeoff and landing-capable personal aerial vehicles. It is anticipated that such a personal aerial vehicle would be flown by a “flight-naive” pilot who has received much less training than is typically received even by today’s general aviation private pilots. The methodology used to determine handling requirements for a personal aerial vehicle cannot therefore be based entirely on existing best practice; the use of highly experienced test pilots in a conventional handling assessment limits the degree to which results apply to the flight-naive pilot. Using rotary-wing handling qualities methods as a start point, this paper describes both existing and newly developed alternative methods to subjectively and objectively analyze the performance and workload of flight-naive pilots in typical personal aerial vehicle tasks. A highly reconfigurable generic flight dynamics simulation model that has been...

An output-feedback control law is designed for the longitudinal flight dynamics of an aircraft. The proposed control law is designed using the adaptive backstepping method and does not require any knowledge of aircraft aerodynamics beyond well-known qualitative physical properties. The resulting feedback controller is able to follow given references in both airspeed and flight-path angle by actuating elevator deflections and aircraft engine thrust. Engine physical limits are incorporated into the design by using a Lyapunov function analysis that includes saturation, obtaining a novel hybrid adaptation law that guarantees closed-loop system stability. Simulation results show good performance of the feedback law and, in particular, demonstrate that the hybrid adaptation law improves the behavior of the closed-loop system when saturations are present. A degraded scenario (a sudden cargo displacement that renders the aircraft statically unstable) is also considered to show the adaptation capabilities of the c...

This work presents the integration of detailed models of a pilot controlling a helicopter along the heave axis through the collective control inceptor. The action on the control inceptor is produced through a biomechanical model of the pilot’s limbs, by commanding the activation of the related muscle bundles. Such activation, in turn, is determined by defining the muscle elongations required to move the control inceptor in order to obtain the control of the vehicle according to a high-level model of the voluntary action of the pilot acting as a regulator for the vehicle. The biomechanical model of the pilot’s limbs and the aeromechanical model of the helicopter are implemented in a general-purpose multibody simulation. The helicopter model, the biomechanical model of the pilot’s limbs, the cognitive model of the pilot, and their integration are discussed. The integrated model is applied to the simulation of simple, yet representative, mission task elements.

International audience; With the growth of civil aviation traffic capacity, safety and environmental considerations urge today for the development of guidance systems with improved accuracy for spatial and temporal trajectory tracking. This should induce increased practical capacity by allowing timely operations at minimum separation standards while at takeoff and landing and trajectory dispersion should be reduced, resulting in better controlled noise impacts on airport surrounding communities. Current civil aviation guidance systems operate with real-time corrective actions to maintain the aircraft trajectory as close as possible to a space-indexed planned trajectory while the flight management system copes indirectly with overfly time constraints. In this paper, the design of new longitudinal guidance laws is considered so that accurate vertical tracking is achieved while overfly time constraints are satisfied. Here, distance to land is adopted as the independent variable for the aircraft flight dynamics since it is today available onboard aircraft with acceptable accuracy. A representation of aircraft longitudinal guidance dynamics is developed according to this spatial variable, and a space-indexed nonlinear inverse control law is established to make the aircraft follow accurately a vertical profile and a desired airspeed. The desired airspeed is defined by an outer space-indexed control loop to make the aircraft overfly different waypoints according to a planned timetable. Numerical simulation experiments with different wind conditions for a transportation aircraft performing a descent approach for landing under this new guidance law are described. The resulting guidance performances are compared with those obtained from a classical time-based guidance control law.

This paper introduces the nonlinearity index theory for assisting aircraft flight dynamics. The nonlinearity index theory was originally developed for orbital mechanics applications within the context of an initial value problem, while aircraft dynamic systems more commonly experience an input excitation as well as sensitivity to initial conditions. This current research proposes an algorithm for applying the index to aircraft dynamics. The algorithm starts by gridding down the flight envelope to a set of points. Around each point, an elliptical subregion is defined as ratios of the altitude and Mach number bands. A set of nominal linear models is then generated at each point. The maximum deviation of each nominal linear model from the equivalent linear models over the local subregion is presented as the basis for various nonlinear index measures. Visualizing these metrics over the entire flight envelope delivers a criterion to predict and identify flight regions of nonlinear phenomena such as limit cycli...

The multibody flight dynamics of flapping-wing micro air vehicles are inherently complex. Stability analyses and control algorithms are best applied to equations of motion in first-order form. This paper presents a method for approximating the first-order equations of motion for a flapping-wingmicro air vehicle. The first-order equations of motion are derived from a coupled, multibody representation of the system. The first-order equations are analyzed using an approximation method called quarter-cycle averaging. The quarter-cycle averaging method is necessary because the classical averaging techniques are not available. The quarter-cycle approximation method is applied to representations of hovering flight and forward flight. The method enables the calculation of equilibrium points for the averaged system.Forbothflight regimes, the quarter-cycle approximatiomethodprovides anorder ofmagnitude improvement in accuracy when compared to local averaging.

Landing Test. An extraordinary array of aircraft were tested during his tenure, including the Douglas Skyrocket D-558-2; X-series airplanes from X-1E through Lifting Bodies; most of the Century Series of fighters; numerous test-bed aircraft incorporating unique technology such as the digital fly-by-wire system, integrated propulsion control system, and supercritical wing; two variable-stability aircraft (F-100C and Lockheed JetStar); the Lunar Landing Research Vehicle; remotely piloted vehicle research, including drones for aerodynamic and structural testing, 3=8-scaled F-15 spin vehicle, and highly maneuverable aircraft technology; and several radio-controlled experimental aircraft now called mini remotely piloted vehicles.

T HIS work investigates the effect of aeroelastic interaction between flexible ornithopter wings and the surrounding airflow on overall flight dynamics and stability. Typical ornithopter wings are composed of carbon rod stiffeners with a nylon fabric skin, providing anisotropic flexibility distribution to the wings. High speed camera images of ornithopter flights reveal that the wings undergo passive deformation both in chordand spanwise directions, and this aeroelastic phenomenon is known to heavily affect aerodynamic forces andmoments of the entirewing [1–6]. However, no studies have adequately addressed whether or not flexibility of wings is favorable to flight stability. Generally, for the analysis of flight dynamics and stability of ornithopters, a complex nonlinear flexible multibody configuration of an ornithopter is simplified to a linear rigid-body dynamics model with a quasisteady aerodynamic model. In particular, the passive deformation of a flexible-wing structure is oftentimes not considered or at best assumed to have a prescribed form to guarantee enough lift and thrust to propel the vehicle aloft [7–11]. Among these relevant studies, Dietl et al. [7] focused on the flight stability of an ornithopter using a single rigid-body model with prescribed sinusoidal twist angle distribution profile of the wings and concluded that the system had an unstable limit-cycle trim condition. This paper addresses the issue of the effect of passive deformation in local twist angles of flexible ornithopter wings and how it influences longitudinal flight stability. Two different ornithopter models were constructed based on the ornithopter flight simulation framework used in previous studies [12,13], which can account for flexiblemultibody dynamics andfluid-structure interaction ofwings. Both models were identical except for the wing structure; the reference model has rigid wings with prescribed sinusoidal local twist angle change as in [7], whereas the other hasflexiblewingswith aeroelastically varying local twist angles resulting from fluidstructure interaction. Longitudinal trimmed level flight and transient response to a pitch directional moment disturbance were compared between the two ornithopter models to ascertain the effect of aeroelasticity. II. Modeling and Simulation Methodology

This paper presents a nonlinear parameter-varying modeling approach to duplicate the aircraft dynamic behavior while moving from one flight region to another. This approach starts by generating a local two-term truncatedVolterra series, which is enough to capture the quadratic andbilinear nonlinearities, at different operating conditions over the flight envelope. The variation of these series’ coefficient matrices are then sought through different interpolation techniques. A nonlinear F-16 longitudinal model was used to assess the proposed approach. The improvement in the accuracy to predict, understand, and analyze the nonlinear aircraft behavior over the previous linear parameter-varying approach, which effectively ignored the second-order stability and control derivatives, is demonstrated through many numerical test cases.

This paper addresses the flapping frequency-dependent trim flight characteristics of a bioinspired ornithopter. An integrative ornithopter flight simulator including a modal-based flexible multibody dynamics solver, a semiempirical reduced-order flapping-wing aerodynamic model, and their loosely coupled fluid―structure interaction are used to numerically simulate the ornithopter flight characteristics. The effect of the fluid―structure interaction of the main wing is quantitatively examined by comparing the wing deformations in both spanwise and chordwise directions, with and without aerodynamic loadings, and it shows that the fluid―structure interaction created a particular phase delay between the imposed wing motion and the aeroelastic response of the main wing and tail wing. The trimmed level flight conditions of the ornithopter model are found to satisfy the weak convergence criteria, which signifies that the longitudinal flight state variables of ornithopters need to be bounded and that the mean value of the variables are converged to the finite values. Unlike conventional fixed-wing aerial vehicles, the longitudinal flight state variables, such as forward flight speed, body pitch attitude, and tail-wing angle of attack in trimmed level flight, showed stable limit-cycle oscillatory behaviors with the flapping frequency as the dominant oscillating frequency. The mean body pitch attitude and tail-wing angle, and the root-mean-square value of the body pitch attitude, decreased as the flapping frequency increased. In addition, the mean forward flight speed is found to almost linearly increase with the flapping frequency.

This paper details the flight dynamics and control of a prototype mono-wing rotorcraft that mimics the passive transit of the species of samara (winged seed), Acer diabolicum Blume. The asymmetric and all-rotating platform requires the development of a novel sensing and control framework. The general rigid body dynamics are separated into rotor dynamics and particle navigation, which are derived for a coordinated helical turn flight path. The equations of motion are used to calculate the forces necessary for flight along a trajectory recorded with a visual motion capture system. The result is a framework for state estimation and control, applicable to scaled versions of the robotic samara.

Hypersonic flightconditionsproducetemperaturevariationsthatcanalterboththestructuraldynamicsand flight dynamics. These aerothermoelastic effects are modeled bya nonlinear, temperature-dependent, parameter-varying state-space representation. The model includes an uncertain parameter-varying state matrix, an uncertain parameter-varying nonsquare (column-deficient) input matrix, and a nonlinear additive bounded disturbance. A Lyapunov-based continuous robust controller is developed that yields exponential tracking of a reference model, despite the presence of bounded nonvanishing disturbances. Simulation results for a hypersonic aircraft are provided to demonstrate the robustness and efficacy of the proposed controller.

This paper presents a recent study to investigate flight dynamics and adaptive control methods for stability and control recovery of a damaged generic transport aircraft. Aerodynamic modeling of damage effects is performed using an aerodynamic code to assess changes in the stability and control derivatives of the damaged aircraft. Flight dynamics for a general aircraft are developed to account for changes in aerodynamics, mass properties, and the center of gravity that can compromise the stability of the damaged aircraft An iterative trim analysis is developed to compute incremental trim states. A neural network hybrid direct-indirect adaptive flight control is developed for the stability augmentation control of the damaged aircraft. The proposed method performs an online estimation of damaged plant dynamics to improve the command tracking performance in conjunction with a direct adaptive controller. The plant estimation is based on two approaches: 1) an indirect adaptive law derived from the Lyapunov stability theory to ensure that the tracking error is bounded, and 2) a recursive least-squares method that minimizes the modeling error. Simulations show that the hybrid adaptive controller can provide a significant improvement in the tracking performance over a direct adaptive controller working alone.

When the towpoint of an aerial cable system moves in a tight circular path, the drogue at the cable tip moves towards the center of the circle, and its altitude decreases relative to its equilibrium position in forward flight. Such a system has both military and civilian applications, including remote pickup and delivery of payloads. This work studies the transitional dynamics of such a system as the aircraft changes from straight flight to circular flight. The system dynamics are modeled using a discretized cable model, allowing the cable to take on zero tension values. Numerical simulation results show that the cable becomes slack during the transition if the aircraft turns too rapidly. Parametric studies of the towpath are performed for both tow-in and tow-out maneuvers. Tension waves can be reduced by appropriate control of the towpoint. Simulated annealing is used to optimize some parameters used to specify the tow-in maneuver. Alternatively, a deployment controller is developed using fuzzy logic that avoids some of these problems by deploying the cable while I the aircraft orbits. Instability of deployment for certain combinations of cable length and length rate are observed.

Full simulation models for flexible air-breathing hypersonic vehicles include intricate couplings between the engine and flight dynamics, along with complex interplay between flexible and rigid modes, resulting in intractable systems for nonlinear control design. In this paper, starting from a high-fidelity model, a control-oriented model in closed form is obtained by replacing complex force and moment functions with curve-fitted approximations, neglecting certain weak couplings, and neglecting slower portions of the system dynamics. The process itself allows an understanding of the system-theoretic properties of the model, and enables the applicability of model-based nonlinear control techniques. Although the focus of this paper is on the development of the control-oriented model, an example of control design based on approximate feedback linearization is provided. Simulation results demonstrate that this technique achieves excellent tracking performance, even in the presence of moderate parameter variations. The fidelity of the truth model is then increased by including additional flexible effects, which render the original control design ineffective. A more elaborate model with an additional actuator is then employed to enhance the control authority of the vehicle, required to compensate for the new flexible effects, and a new design is provided.

The effectiveness of open-box micro air vehicles to deliver light, small payloads of high importance to specific ground coordinates is investigated through dynamic simulation. The open box exhibits interesting and varied flight dynamic behavior as key design parameters are changed. For example, the open box can achieve a coning behavior, a corkscrewing behavior, or glide much like a conventional aircraft to the ground by merely shifting the mass center location. The four rear flaps of the air vehicle can be used to control the box and affords the aircraft greater control authority than dispersion caused by typical atmospheric winds. This control mechanism can also be used as a braking system, which can greatly arrest the descent rate before ground impact. These dynamic qualities make the open box a promising airdrop vehicle which can cut through atmospheric winds towards the target before decelerating and gently landing.

In this paper, we consider the equations of motion of a two-spacecraft formation flying array that uses electromagnets as relative position actuators. The relative positions of the spacecraft are controlled by the forces generated between the electromagnets on the two spacecraft, and the attitudes of the spacecraft are controlled using reaction wheels. The nonlinear equations of motion for this system are linearized about a nominal operating trajectory, taken to be a steady-state spin maneuver used for deep-space interferometric observation. The linearized equations are analyzed for stability and controllability. Although the open-loop system proves to be unstable, a controllability analysis indicates that the system is fully controllable with the given suite of actuators, and is therefore stabilizable. An optimal linear feedback controller is then designed, and the closed-loop dynamics are simulated. The simulations demonstrate that the closed-loop system is indeed stable, and that linear control is a very promising technique for electromagnetic formation flight systems, despite the nonlinearity of the dynamics.

Formation flight is a known method of improving the overall aerodynamic efficiency of a pair of aircraft. In particular, one craft flying in the correct position in the vortex wake of another can realize substantial reductions in drag, with the amount of the reduction dependent on the relative positions of the two craft. This paper looks at such a pair, with one craft flying behind and to the side of the lead plane. The precise position of the second craft relative to the first to maximize the drag reduction is to be determined online, leading to a peak-seeking control problem. A new method of speak-seeking control, using a Kalman filter to estimate the characteristics of the drag reduction, is derived and discussed. A simple model of the two-plane formation using horseshoe vortices is defined, and the peakseeking controller is applied to this model. The method is demonstrated in simulation using this simplified model. S an airplane flies, it causes an upwash ahead of the wing and leaves a wake behind. This wake is characterized by the downwash behind the wing and by an accompanying upwash in the area on either side of the downwash region. By flying in the area of upwash, a second aircraft can gain a substantial efficiency boost because of the reduction in induced drag it will experience. This leads to the well-known fact that two aircraft flying in an appropriate formation can achieve overall efficiency much greater than were they flying separately. 1 This effect is analyzed using inviscid aerodynamic assumptions and lifting-line theory in Ref. 2, where it is noted that the effects were considered by Munk as early as 1919. The theory was put to test in actual aircraft by Hummel, 3 who established a fifteen per cent reduction on the second of a pair of civilian aircraft. Because of the gains in efficiency, formation flight has been investigated as a way of increasing the range and duration of autonomous aerial vehicles. In Refs. 4 and 5, formations of several aircraft are considered, with the object of creating a solar-powered formation that could cruise at high altitude for arbitrarily long times. In Ref. 4, decentralized controllers are derived for a formation of five highaspect-ratio craft and are shown to be capable of maintaining a prescribed formation despite the nonlinear, destabilizing moments induced on each plane by the aircraft ahead of it in the formation. The formation maintenance problem for a pair of F-16 class aircraft is considered in Ref. 6, though that paper relegates the rolling moments on the trailing craft to an inner-loop controller and considers only the lift and side force in designing an autopilot for the trailing plane. In this paper, only a pair of aircraft is considered. The two craft can be thought of as a leader and a follower. The leader flies straight

Introduction A TOPIC of classical interest in atmospheric flight dynamics of a landing aircraft or lifting-body vehicle is the synthesis of flight path from an arbitrary initial point to a terminal point with a desired final velocity vector direction. This problem has been extensively analyzed in the published literature.1−3 In a sense, similar problems can be considered for a mobile body such as an automobile, mobile robot, floating point, etc. Proportional navigation is a well-known homing interception guidance law4−6 for which the velocity vector (heading) of the interceptor is turned at a rate proportional with a navigation ratio λ to the rotation rate of the line joining the interceptor and moving target, which is the line of sight. As a rule, for the intercept trajectories the navigation ratio is held fixed. It is evident that the proportional navigation is acceptable for the nonmoving targets. In this case, the navigation ratio can be considered as a control variable, which depends on the current and desired final states. This Note presents a terminal guidance law to find a vehicle trajectory with the specified heading at the desired final point.

Introduction F ROM the beginnings of the evolution of flight, there evolved an appreciation of the advantages of an aircraft that was easy for the pilot to fly. Among the insights for which they are famous is the Wright brothers’ realization that when the ability to balance and steer became understood, then aviation would truly have arrived. As the balance between stability and control became better understood, aircraft emerged with sufficiently good flying (or handling) qualities to allow air-to-air combat, reliable passenger transport, and a host of other uses. As aeronautical engineers examined the measurable factors that seemed to bestow good flying qualities, they followed the urge of all engineers, which is to write down those lessons, rules of thumb, and guidelines that make the job easier the next time. From the observations of these engineers, and especially from dedicated research using special-purpose variable-stability aircraft, the community began to document characteristics that were preferred for good flying qualities, along with characteristics that would indicate poor qualities. Most of the early flying-qualities work involved essentially steady-state characteristics like stick force variation with steady, trimmed speed. Dynamic behavior was not so well understood, though early aviators did comprehend the slow tradeoff between altitude and speed in Lanchester’s phugoid mode. They also knew all too well the sinister origins of the slow divergence called the spiral mode. The quick lateral-directional oscillations of the Dutch roll were commonly experienced. Appreciation of the rigidbody modes of motion greatly improved in the first half of the 20th century, including the faster lateral roll mode and the quick angle-of-attack oscillations of the short-period mode. By the middle of the 20th century, engineers realized that the time constants, damping ratios, and natural frequencies of all of these modes could be correlated with flying qualities, good or bad. The stage was set for formal requirements, in the form of military specifications, to define the good and bad values of these modal parameters.

In Part 1, equations of motion for boomerang flight dynamics were presented in strictly nonlinear form and solved numerically for a typical returning boomerang. The solution shows that the motion consists of both long- and short-period oscillations. These oscillations were found to be the result of the aerodynamically asymmetric moment and the gyro effect of the spinning motion with high advance ratio. When either the initial conditions at takeoff or the geometrical characteristics of the boomerang were varied, various flight paths and flight performances were obtained, some of which are compared with experimental results. The detailed mechanisms of the returning path, tennis racket effect on the flight stability, and ways of throwing a boomerang to avoid dangerous flight path are presented.

The paper proposes a reconfigurable flight-control system for the tracking of altitude, heading, sideslip, and velocity commands. The control law can serve for the command of unmanned air vehicles or as an autopilot for piloted aircraft. The inner core of the algorithm consists of a reconfigurable control system providing tracking of pitch-, roll-, and yaw-rate commands. It is based on a model reference control law and a stabilized recursive least-squares algorithm. The outer loop is based on a linear design, with compensation for the nonlinear couplings arising from flight dynamics. Some parameters of the outer loop are identified in real time in order to adapt to varying flight conditions. The algorithm is evaluated using a nonlinear F-16 simulation model. The results demonstrate the consistent performance of the algorithm through various flight conditions, as well as its turn coordination capabilities, its reconfiguration after a floating left elevator failure, its ability to move across the power curve, and its tolerance to measurement noise and turbulence.

Bifurcation theory has been used to study the nonlinear dynamics and stability of many modern aircraft, especially in broad angle-of-attack e ight dynamics. However, the main application of bifurcation analysis is based on numerical simulations to predict and explain the nonlinear instability of e ight dynamics by the use of parametric continuation methods. Bifurcation theory is applied to theoretically analyze the nonlinear phenomena of longitudinal e ight dynamics, by the choice of the elevator dee ection and mass of the aircraft as system parameters. Both stationary and Hopf bifurcations may appear at some critical values of elevator command. Discontinuity also may occur at system equilibria as system parameters vary. The bifurcation phenomena occurring in nonlinear aircraft dynamics might result in jump behaviors, pitch oscillations, or system instabilities. Numerical study of a simple third-order model of longitudinal dynamics verie es the theoretical analysis. Qualitative results are obtained to understand the longitudinal e ight dynamics.

References 1Lanchester, F. W., Aerodonetics, Archibald Constable, London, 1908. 2Etkin, B., and Reid, L. D., Dynamics of Flight: Stability and Control, Wiley, New York, 1996. 3Nelson, R. C., Flight Stability and Automatic Control, McGraw–Hill, New York, 1990. 4Roskam, J., Airplane Flight Dynamics and Automatic Flight Controls, Vol. 1, Roskam Aviation and Engineering Corp., Lawrence, KS, 1979. 5Pradeep, S., “A Century of Phugoid Approximations,” Aircraft Design, Vol. 1, 1998, pp. 89–104. 6Ananthkrishnan, N., and Unnikrishnan, S., “Literal Approximations to Aircraft Dynamic Modes,” Journal of Guidance, Control, and Dynamics, Vol. 24, No. 6, 2001, pp. 1196–1203. 7Phillips, W. F., “Phugoid Approximation for Conventional Airplanes,” Journal of Aircraft, Vol. 37, No. 1, 2000, pp. 30–36.

Results are presented from a study of time-optimal attitude reorientation maneuvering for an aircraft with thrust-vectoring capability. A detailed mathematical model for attitude motions of the aircraft is developed. First-order necessary conditions for optimality are applied and a family of extremal solutions obtained for two classes of reorientation maneuvers of practical interest. The thrust-vectoring power is varied parametrically, and thus an estimate of the reduction in maneuvering time due to the thrust-vectoring enhancement of the aircraft is obtained. ARIOUS analyses have shown that emerging trends in missile and radar technologies will have a profound effect on design requirements for air-superiority vehicles. It appears that, in close-in combat, vehicles with the ability to operate at extreme angles of attack will have a decided advantage.1'4 Designing such supermaneuverable aircraft is a complex and challenging task, and future design efforts may well lead to radically new concepts. At present, however, the preferred approach is to provide a form of thrust vectoring in which propulsive power is used to generate control moments.5'6 At high angles of attack a, especially in the post-stall region, the effectiveness of the aerodynamic control surfaces decreases rapidly with increase in a.. Thus, thrust-vectoring generated (propulsive) moments must be used to maintain control of the aircraft at high a. At low a the propulsive moments can supplement the aerodynamic control surfaces and thus increase the "agility" of the aircraft. In addition, thrust vectoring can be used for control of the aircraft in case of mechanical failure or malfunction of the aerodynamic control surfaces. Several research programs that focus on utilizing thrust-vectoring control are currently under way. Among these is the F/A-18 based High Angle-of-attack Research Vehicle (HARV) program.7 The flight mechanics issues can be divided into two areas: 1) analysis of changes in the velocity vector and 2) analysis of changes in the body attitude. This paper presents some results obtained in a study that focused on understanding the nature of aircraft minimum-time fuselage-reorientation maneuvering. In the study, data for the HARV were used. Accordingly, the numerical results correspond to this aircraft. However, the discussion and methodology in analyzing the results presented in the next sections are quite general. A mathematical model of the aircraft and the interacting environment (the aerodynamic forces and moments) is derived in Sec. II. The basic ideas and assumptions in the development of the mathematical model are discussed in detail. In Sec. Ill a class of optimal control problems of interest is formulated and a set of necessary conditions for optimality derived by using the Minimum Principle.8'10 This set of necessary conditions is cast into a numerical multipoint boundary-value problem (MPBVP). Subsequently, a homotopy method and the related procedure for solving the MPBVPs (and thus generat

A new concept of sequentially dispensing submunition from a spinning dispenser is described. Flight dynamics of a weapon system based on this concept was simulated to investigate its flight characteristics and its ability to create both linear and curved impact patterns over the target. Performance of such a weapon is illustrated by considering both cruise missile and ballistic-type launch trajectories. Effects of varying launch conditions and ejection strategy as well as flight path disturbances on the weapon performance are presented. It is shown that this dispensing concept has the potential of growing into a versatile weapon system.

The present investigation is concerned with an examination of optimal symmetry flight on the basis of the intermediate vehicle model. The analysis is partly based upon an exploration of Euler solutions for the path-angle-as-control model carried out by Kelley (1958). The current analysis takes into account higher-order optimality conditions and "chattering-control' phenomena. Attention is given to details regarding the intermediate vehicle model, the Legendre-Clebsch necessary condition, the conjugate-point test, and the numerical solution of the time-range problem. It is found that the flight path angle takes on the role of control variable in the model. From physical considerations, it can be seen that when a positive margin of thrust over drag exists, the maximum-range climb trajectory without time or fuel constraints has no proper maximum nor an upper bound.