The warship continues to move after the trajectory correction projectile is fired from shipborne gun, and the shipborne radar for trajectory measurement also continue to move and sway, and so the rela- tive trajectory measured by radar need to be transformed into the ballistic reference frame which takes the gun muzzle as an origin during firing. The precision of transformed ballistic coordinates is influenced by the warship fluctuation and the errors of radar measuring, warship sway angles, velocity and course bear- ing. In order to quantify the influence of every error on the precision of ballistic coordinates, a model of precision of ballistic coordinates was set up and simulated, and some data about the influence of warship fluctuation and the errors of radar measuring, warship sway angles, velocity and course bearing on the precision of ballistic coordinates were got.

In order to ensure high dispersing velocity of the submunitions in the low overload dispersing environment, a new piston central dispersing mechanism was devised and working process of the dispersing mechanism was researched. The characters of this kind of mechanism were as follows: the trust force from the piston to the submunition was transmitted by the beveled sabot; the powder burned in the highpressure chamber and the generated powder gas did work in the lowpressure chamber; the initial trust peak was reduced, and so on. According to the working principle of the piston central dispersing mechanism, the force analysis of piston, sabot and submunitions were carried out, and the interior ballistics model of the new mechanism was established. It is proved by the simulation calculation that, this new piston central dispersing mechanism not only can supply a dispersing velocity more than 50m/s, but also can control the overload of submunitions under 1000g. The interior ballistics model can be used to guide the design of the new piston central dispersing mechanism.

The concept of dual-spinning becomes a new approach to upgrade a conventional spin-stabilized projectile, wherein an actuator is used to control the phase of forward canards. To design and analyze the inner control channel efficiently, a dual-spin ordinary differential equation, including a quasi-steady aerodynamic model and an optimized LuGre friction model, is established. All aerodynamic and kinematic data in time-domain, as input in least square estimation, is obtained in transient numerical model and dynamic wind tunnel test. The results indicate that the side force and roll moment supplied by canards are affected by phase angle and roll rate, and the estimated accuracy of quasi-steady aerodynamics is lower than 4×10^-3. The friction between forward and aft parts is a function of axial pressure and relative roll rate, which can be estimated by the optimized LuGre model. The feasibility of using the dual-spin model to predict the canard movement is validated by measurement in a flight test. The proposed approach promotes the pace of engineering application of dual-spin projectiles.

Considering that the length of the tubular charge for the large caliber high speed Davis gun is long, the traditional pseudo-fluid hypothesis in two-phase flow model may cause errors. In order to solve this problem, Eulerian coordinate system is used to settle the gas field, and the Lagrangian coordinate system is used to settle the solid field. It is assumed that the tubular charge clusters are linearly configured along radial direction, these clusters move along axial direction，and gas moves along radial and axial directions. Based on this assumption, a two-dimensional interior ballistics model is established for a 480 mm Davis gun with tubular modular charge. Then through the comparison of the simulated and experimental results, the proposed model is verified to be effective. The distribution of gas pressure along two directions and the movement rules of tubular charge clusters along axial direction were obtained by further analysis of the simulated results.

An interior ballistic model is established on the basis of modified corresponding virial equation for the high-pressure air ejection device under the wide variation conditions of pressure and temperature. The second and third virial coefficients of modified corresponding state equation are calculated. Based on the virial equation of volume series form which is truncated to the third virial coefficient, the analytical expressions of specific thermodynamic energy and specific enthalpy are presented, and the dynamic ther- modynamic parameters are obtained. The numerical experiments are performed. The changing rules of thermodynamic properties and missile acceleration and velocity are obtained. The results show that the compression factor reaches 1. 107, and both the actual decreased values of temperature and pressure are higher than the ideal decreased values in the hyperbaric chamber, and the work capability of hyperbaric air deviates from the ideal gas, and it is necessary to study real gas effects.

Converting and evaluation methods for submarine-launched interior ballistic functional test are summarized: according non-design condition and small trial sample status. A method is put forward to convert the functional parameter of submarine-launched interior ballistic by developing a simulation software and estimating the environmental factor among normal samples with Monte-Carlo way. Evaluation method of interior ballistic functional parameter is also set up. Based on this method, the exact main environmental factors are defined by choosing multiple regression way, which can be used to comprehensively analyze the influence factors of functional parameter , and to improve the estimation precision of normal environmental factors. The composition of simulation and estimation software system and the design method of simulation experiment are described in detail.The simulated and estimated results of condition factor among normal samples are given by taking the environmental factor of velocity for example.

The working condition of barrel forcing cone is worse during the firing process of small arms. To study the influence of the forcing cone angles on the stress of barrel forcing cone, the three-dimensional finite element models of barrel and projectile at different forcing cone angles are established, in which the structures of barrel and projectile, and nonlinear constitutive relations are considered. The effects of different forcing cone angles on the projectile engraving process are analyzed. The data of engraving resistance is obtained under the condition of different forcing cone angles. A response surface model of engraving resistance is established. The formula and the variation rules of projectile engraving resistance along with the forcing cone angle and engraving displacement are calculated based on the above data by using Hermite polynomial. A dynamic model of projectile engraving process is established in consideration ofthe engraving resistance. The engraving pressure during the projectile engraving process is solved by programming. The forcing cone angles among 0.11° and 1.13°, which satisfy the requirement of muzzle velocity of the projectile, are obtained, and then the best forcing cone angle of 0.56°, which could reduce the barrel stress to ensure the highest velocity and meet the design range of forcing cone angles in case of satisfying the interior ballistic behaviors, is got.

The evaluation of penetration effectiveness of ballistic missiles under the cover of decoys is an important issue. The missile penetration probability is used as an evaluation index of penetration effectiveness. Based on the different decoy jamming and anti-missile interception strategy, the penetration effectiveness models of single and multiple ballistic missiles are built. Considering the effect of decoys, the penetration effectiveness of multiple ballistic missiles is quantitatively studied. At last, the results of a sample are analyzed, and the models are verified, from which some valuable conclusions are got. The research result has a certain reference value to the simulation and evaluation of penetration ability of ballistic missile.

In order to explore the interior ballistic characteristics of liquid propellant mortar, a 60 mm liquid propellant mortar transient measurement system was developed to measure the pressure in combustion chamber and the muzzle velocity of mortar shell. Based on the experiment, a two-phase flow model with combustion reaction for liquid propellant mortar is established by using unsteady Eulerian-Lagrangian model and liquid propellant evaporation-combustion model. The coupling relationship between the complex gas phase flow field and the injection-combustion of liquid propellant as well as the formation mechanism of pressure oscillations are analyzed by simulating the reaction flow field during the interior ballistic process. The results show that the 60 mm liquid propellant mortar has excellent combustion stability. The numerically simulated results are in good agreement with the experimental results, where the experimental pressure oscillation is repeated, proving that the established model is reasonable and reliable. Both injection and combustion of liquid propellant are affected by gas vortex in combustion chamber. The concentrated combustion caused by the reflected waves makes the pressure appear as an oscillatory development.

The ballistic trajectories of projectiles with differently shaped noses and composite material noses obliquely penetrating into steel target are researched. The deflection torque during the penetration is also studied. The results show that the ballistic deflection ofprojectile with truncated-oval nose is smaller, its performance against the ballistic degradation is high and its penetration trajectory is stable. The nose made of high-density and high hardness tungsten composite material shows the better penetration performance and the smaller ballistic deflection angle. The deflection relevance of oblique penetration ballistic trajectory is obtained based on the relation between the oblique torque and the oblique angle. It can be seen from orthogonal experiment simulation that the shape of the nose, the material of the nose and the penetrating velocity have the effects on the oblique angle.

The extended weighted and object functions are proposed based on the time-to-go exponential function. The optimal control theory is used to deduce a family of extended optimal trajectory shaping guidance laws for the constant maneuvering target. According to Schwartz inequality, the analytical solution of the guidance law acceleration command is derived by introducing the initial displacement, initial heading error, target maneuver and final impact angle into the lag-free guidance system. The analysis shows that the final acceleration command approaches to zero when the exponent of the time-to-go exponential function is greater than zero. The non-dimensional position and angle miss distance of guidance system with first order lag are studied using the non-dimensional method and the adjoint method. The results show that the position and angle miss distance induced by the heading error and final impact angle approach to zero when the missile terminal guidance time is about 15 times of the system lag time constant. And also, the position and angle miss-distance are smaller when the signs of initial heading error angle and final impact angle are opposite.

For the technical scheme of the two-dimensional trajectory correction projectiles (TDTCPs) with drag brake and despining blade, the mathematical model of two dimensional trajectory corrections is discussed based on the theory of exterior ballistics. An approximate formula for predicting the ballistic drift and trajectory correction quantity is deduced with respect to the process of lateral trajectory correction. The capability of lateral trajectory correction and the flight stability of TDTCP are also analyzed. By comparing with the results of flight test, the accuracy and effectiveness of this approximate calculation method are verified. The result of the approximate method is in accordance with those of 6DOF trajectory model and firing test, and the maximum error is no more than 40 m. All the work is valuable for further research.

A three-dimensional two-phase flow model based on arbitrary Lagrange-Euler method is established to improve the computational accuracy and cost of three-dimensional simulation for interior ballistic in guns. The three-dimensional governing equations are discretized with the MUSCL scheme. The fourth-order Runge-Kutta method is used to solve the time orientation. The numerical method is coded and compiled in the MPI parallel environment. The numerical simulation shows the detailed three-dimensional development of the two-phase flow behavior. The calculated results are in good agreement with the results in Ref.［20］. The effects of different igniter lengths and diameters on interior ballistic performance are analyzed. Parallel numerical studies show that the parallel efficiency can be reduced by about 50% using interior ballistic three-dimensional calculation of 24 processes. Key

The stability criteria related to the structure parameters of correction fuze are derived based on the simplified model and engineering methods for the aerodynamic characteristics of wing-body combinations, Murphy’s complex variable method and the Hurwitz stability theory. The influence of structure parameters of correction fuze on the stability of spin-stabilized projectile is analyzed for the design and optimization ofcorrection fuze. The stability analysis demonstrates that the forward movement of mass point of the combinations through the balance weight or the structure optimization of correction fuze is in favor of stability when the boundary dimensions of correction fuze (except for the canards) are the same; the increase in the deflection angles of canards is better than the extension of wingspan in order to increase the correction force while reducing the effect on stability. The simulations and experiments verify that the flight stability of projectile can be enhanced by moving the mass point of the combinations forward. Key

To get the surface temperature characteristics of projectile flying at high rotational speed, based on the six degree of freedom (6-DOF) rigid body trajectory model, the heat balance equations were established by using node thermal network method. With the heat exchange theory of flow around a cylin- der, the influence of rotation was considered for the calculation of aerodynamic heating. The temperature field distribution under the control of trajectory data and airflow properties was obtained by solving the trajectory equations and the heat balance equations simultaneously. Finally, the factors which have im- pact on the surface average temperature field, including launching velocity, initial rotational speed, launching angle and airflow temperature, were also studied. The results show that the surface temperature increases with launching velocity non-linearly. The temperature gradient is inversely proportional to the distance from the warhead. The bigger the initial rotational speed is, the higher the peak temperature and the rate of temperature change are. The higher the airflow temperature is, and the smaller the launching angle is, the higher the average temperature is.

In order to improve the simulation precision of artillery interior ballistics, on the base of the artillery erosion interior ballistics theory in Ref.\[1\], thekinetic equation of projectile and the basic equation of interior ballistics are set up by keeping the equations of the variable projectile starting pressure, and the geometric combustion law and burning rate law of gunpowder unchanged, and analyzing the full-bore erosion wear characteristics of artillery, such as variable bore sectional area, variable chamber volumeand volume increment after body, and then an interior ballistics model based on the whole-bore erosion wear is established. The resolving method of interior ballistics is derived. The certain artillery test data are computed through simulation. The simulated results demonstrate that the error simulated and test velocities are less than 0.9%, which satisfies the requirement of 3% simulation error of artillery engineering practice. The proposed method is better than the artillery erosion interior ballistics theory in Ref.\[1\]. The result proves that the proposed interior ballistics model and resolving method have higher simulation precision, and could be used for the prodiction of artillery barrel life. Key

The problem of optimizing the maximum range of a glide guided bomb is studied based on the principle of solving optimal control problems using the Radau pseudo-spectral method. The dynamic model of the guided bomb is nondimensionalized. Combining with the Pontryagin minimum principle, the analytic solution of the optimal control and the first-order necessary condition are derived. The trajectory optimization problem is translated to a nonlinear programming via the Radau pseudo-spectral method. Based on covector mapping principle, an optimality verification method is presented for the numerical solution. Simulation results show that the Radau pseudo-spectral method can provide a highly valuable optimal solution for engineering application. Compared with the conventional maximum lift-to-drag ratio gliding trajectory, the trajectory after optimization can be extended by more than 10%.

The aerodynamics of trajectory correction projectile (TCP) could be expressed as the function of geometry and flight state, of which model can decide the accuracy of the dynamic system directly. An engineering model suiting for the trajectory correction projectile with decoupled canards (TCPDC) is established based on the results of wind tunnel test. This model, including drag, lift, side force and pitch moment, takes the effects of complex angle of attack (AoA) and the phase angles of canards into account. The least square method is utilized to identify the parameters, and the predicted results are validated by CFD. The results show that the yaw drag caused by canards is relatively small and the error of TCP’s drag fitted by symmetry model is lower than 3.3% within the small AoA. Under the effects of complex AoA and the phase angles of canards, the lift keeps the sinusoidal feature while a secondary sinusoidal vibration arises along the curve of side force for γ_P=180°. The innovative aerodynamic model makes a foundation for the research on TCPDC’s flight characteristics.

How to design and deploy the interception schemes to meet the specific high-level defense objective is discussed. A correlation between defense objective and the number of interceptors is established based on Bernoulli trial model, and the effects of system generalized tracking ability and single-shot kill probability on the number of interceptors are analyzed as well. the factors, such as high-level defense objective, target number and single-shot kill probability, that affect consumption of interceptors at the modes of salvo fire and string firing are discussed. At the premise of defense objective, the interceptor allocation in a layered defense is modeled as an optimization problem. The average number of consumed interceptors can be minimized by optimizing the quantity of interceptors against the targets in each defense layer.

To improve the adaptabilities of reconnaissance and attack of multi-MAVs, the trajectory of multi-MAVs for coveraging the multi-targets in non-cooperative manner is modeled. The take-off point coordinates of MAVs are simulated using cloud model, and the taking-off direction is simulated by Monte Carlo method. The target zone model, MAV detection model, take-off point model, flight direction model and trajectory model are established. To improve the efficiency of the optimization design, the minimum number of simulations is determined based on the stability analysis of the expected coverage. The multi-target problem is solved by MOGA, and the regional coverage trajectory of multi-MAVs in non-cooperative manner is determined. The problems that can be solved by the schemes are analyzed according to the ratioof detecting radius to target zone radius. The designed trajectories reduce difficulty in control, and take coverage, the number of MAVs and flying range of MAV into account.

An improved two-phase flow model is established to simulate the interior ballistic characteristics of modular propellant charge. In this model, the constraint of the walls of modules on gas flow is taken into account. The rupture rule of combustible case and the flame spreading between different modules are also considered in the improved model. This model turned out to be reliable by comparing the numerical results with the experimental data. It can be used to predict the development of pressure waves and to diagnose the interior ballistic performance of modular propellant charge systems. The simulation results show that the flame spreads slower because the gas is constrained by the bottom walls of the center-tube. The combustible cases are ruptured in sequence, the time when the combustible cases begin to rupture until all the cases rupture is affected by the strength of the modular case and the ignition core.

The nutation angle of projectile is one of the important factors which influence the firing dispersion, and has been a hot issue in the gun research field. In order to get the measurement result of nutation angle near the exit position of projectile, the trajectory tracking method with high speed photography is used to research the nutation angle of projectile. A trajectory tracking system is presented with the high speed photography and the trajectory tracking mount. The image of the projectile flight trajectory is recorded, and the nutation angle of the up-and-down nutation of projectile is got by means of the image analysis software. An example of a gun projectile is demonstrated with the trajectory tracking system, and the rule of up-and-down nutation of projectile near exit position is obtained. The data dispersity of nutation angles for different projectiles is large, and the maximum nutation angle of the first projectile is -5.2°. It is shown that the trajectory tracking method is a perfect method for getting the measurement result of the nutation angle.

An optimal midcourse trajectory correction algorithm considering the zeroing effort interception is designed for the defensive combat in near space. The zeroing effort interception condition is derived by analyzing the relative motion of interceptor and target in the terminal guidance phase, which is uniquely determined by the velocity ratio of target and interceptor and the respective angles among their velocity vectors and the line-of-sight. In terms of the cases where the nominal trajectory fails to satisfy the zeroing effort condition due to the updated target information, a scheme of optimal trajectory correction in the midcourse guidance phase is proposed to modify the interceptor states to re-satisfy the zeroing effort interception condition at the handover moment in the midcourse and terminal guidance phases. The compensation commands of control are derived by further differentiating the first order optimal conditions and transversality conditions that are satisfied by the nominal trajectory. The deviations of interceptor initial states and terminal constraints are considered in the resolving of compensation commands. The simulated results testify the effectiveness and the superiority of the proposed method.Key

In order to numerically simulate the terminal effect of bullet and fragment, the research status of ballistic gelatin physical properties is summarized firstly. The features of rate-dependent hyperelastic model and elastic-plastic hydrodynamic model are studied, respectively. The coefficients of equation of state of ballistic gelatin are concluded based on related experiments. The penetration of a steel sphere into a block of ballistic gelatin is studied experimentally, and is modeled using the finite element method. The comparison of the computed and experimental results shows that the elastic-plastic hydrodynamic model can simulate the experiment more accurately at high velocity impact. Ballistic gelatin is known as a rate-dependent sensitively material, but the thermal softening is dominant at high strain rate, the physical behavior can be modeled with a dynamical constitutive.

In order to study the dynamic interaction process of bearing band and barrel, a thermo-mechanical coupling finite element analysis (FEA) model is established. The engraving process of bearing band and interior ballistic process are simulated by the explicit finite element method with the use of Fortran subroutines. The FEA model is proved to be effective by comparing the calculated results with experimental results. The calculated results show that the coefficient of secondary work varies as a function of time, and an extremum value appears in the early time when using classical interior ballistic equation.The thermal softening of bearing band surface has a significant effect on the interior ballistic process during the band engraving. For fixed cartridge case,the computational accuracy of the engraving process and the interior ballistic process could be improved by taking account of extracting bullet force.

The experiment about the four geometries are carried out. A digital high-speed camera is used to record the evolution of the water-entry process and cavity shapes. The flat-trajectory curves of the four different geometries are obtained, and the effects of the head shape, entry angle and velocity on the trajectory are analyzed . The results show that the projectile body with oval-beveled warhead is easier to form the curved trajectory because of its special warhead. The other three kinds of trajectories are more stabilized. When it is at certain speed range, the trajectories verge to be linear; when it is at a higher speed, the trajectory may be curved. The effect of entry angle on the trajectory is obvious. When the entry angle is little, its trajectory deflects to the free surface quickly; when it is larger, the trajectory deflects to the bottom of the cylinder. The conclusions provide reference for the research on the water-entry weapons.

According to Navier-Stokes equation and Spalart-Allmaras turbulence model，the motion law of projectile under the action of high- pressure gas and its flow characteristics are simulated by using the dynamic mesh method based on CFD software. The change rules of in-bore average pressure， projectile base pressure， chamber base pressure and projectile motion parameters at the four kinds of initial pressure in the chamber are mainly studied. The changes of Mach number contours at different time at initial pressure up to 2.5 MPa are analyzed. Research results show that a flow oscillation phenomenon occurs in the bore，and the changes of chamber base pressure and projectile base pressure are fluctuating. Initial gas chamber has the effect on the pressure oscillation amplitudes of chamber base and projectile base and the projectile in the muzzle velocity. The relationship between projectile motion velocity or motion time and motion distance in the barrel is approximately parabolic.

In the firing accuracy and dispersion test of rapid-fire weapon, several projectiles fired from a barrel may pass through a light-screen simultaneously. On this condition, some photoelectric target measurementsystems cannot measure the exterior ballistic parameters of these projectiles. A qualitative analysisof this phenomenon should be undertaken to obtain the measured values for choosing a reasonable photoelectric target measurement system. The reduced mathematics description of the phenomenon is presented. The two mathematical models for the probability passing through the screen are established, respectively, based on certain and uncertain velocities of the flying projectiles. The change rule of the passing probability with projectiles’ flight distance is deduced according to the optimization mathematical model, and the three important parameters, such as critical distance involved in the passing probability, maximum probability and passing probability at direct fire distance. Experiments show that the reasonably chosen photoelectric target measurement system can avoid the measurement data being influenced by the projectiles passing through a screen simultaneously. Key

In order to achieve the launch of individual rocket in limited space, a individual rocket launching system of which the liquid column is placed in the tail tube as a balance body is proposed. The system is tested, and the interior ballistics process is analyzed over time intervals. Based on the theory of the classical inrerior ballistics theory, a mathematical model of the launching system is established by assumoffing that the irregular mixing of gas and liquid is regarded as mixing of perforation. Runge Kutta method is used for numerical calculation, and the complete curves of interior ballistics process are given. The analysis result shows that the theoretical results are in good agreement with the experimental results. The relative error of the maximum pressure in combustion chamber is 1.6%, and the relative error of projectile velocity is 0.9%. The calculated results shows that the liquid column can be used to reduce the launching characteristics of rocket, improve the velocity of projectile, and enhance the power of individual rocket for the individual rocket launching systems with and without liquid column under the same launching conditions.Key

An “inverse” unscented Kalman filter (UKF) algorithm with seven-dimensional state vector is proposed to solve the problems of low target positioning accuracy and poor fire direction ability of firefin-derradar. A state model is established by taking the ballistic coefficient as the state parameter and incorporating it into the filtering process. The UKF algorithm is used to improve the nonlinear estimation accuracy. The model error accumulates due to the long extrapolated distance of forward filtering.In the proposed algorithm, an inverse filtering is used, the first point measured by radar is used as the end point of the filter, and the artillery position is extrapolated using the fourth-order Runge-Kutta equation. The simulationresults show that the proposed algorithm can effectively improve the extrapolation accuracy of artillery locating and fire correction radar. Key

When a homing missile tracks a target, it may fail to lock the target because of complicated background. For example, when a missile attacks a target in look-down mode, the missile’ capability of intercepting or acquiring a target is weakened by complicated surface background and clutter. A new modeling method which regards the ideal line-of-sight as the control objective is put forward. And an optimal guidance law is designed based on restraining the terminal direction of relative motion between missile and target and the trajectory overload. The guidance law is used to control the motion of missile in a direction vertical to ideal line-of-sight. The simulation result shows that this method can meet the requirement of terminal trajectory shaping better, distribute the overload more reasonably and decrease the influence of ground background and clutter on target tracking effectively.

Realizablek-ε turbulence model, dynamic mesh update method and finite-rate/dissipation model are used to establish an initial cavity secondary combustion flow model with missile movement for research on the influence of combustion product properties on gas-ejection secondary combustion, interior ballistic and load characteristics. The effectiveness of gas ejection model is proven by comparing the calculated data with the experimental data. The influences of combustion product pressure in gas generator inlet and component concentration on gas-ejection interior ballistic and load characteristics are analyzed. The variation ranges of inlet pressure and concentration ratio are obtained. The numerical results show that, with the increase in inlet pressure，the times of O₂ exhaustion and the time out of tube decrease, and the velocity out of tube and the acceleration peak value increase. With the increase in the concentration ratio of CO and H₂, the time of O₂ exhaustion increases, the time out of tube is extended, and the velocity out of tube and the acceleration peak value decrease.

A kind of one-side ejection device with two-step cylinder is proposed to increase the effective thrust travel of missile pneumatic launching system. The real gas state equation, Peng-Robinson equation, is used as theoretical basis. The mathematical expressions of pneumatic interior ballistics model are deduced on the basis of 'P-R' state equation for the two-step cylinder. The interior ballistics equation is solved by using Simulink software, and the one-side launching ejection is built by means of ADAMS. The co-simulation model of device is achieved. The results show that the pressure of first-order lower-chamber rises first and then falls. It can be seen from the calculated result that both the thermodynamic parameters and the missile acceleration obviously fluctuate in the process of cylinder changing, but their influences on missile speed and displacement are very small. To reduce the equipment volume, the air source volume is selected as the objective function. The air source volume optimized by genetic algorithm is decreased by 64.5%, thus improving greatly the mobility of launcher. Key

Some microDoppler features of ballistic missile precession with frequencystepped chirp signal (FSCS) were analyzed theoretically. Combined with compressed sensing (CS) theory, a new method of microDoppler spectrum reconstruction method based on sparse FSCS was proposed. The spectrum information can be reconstructed exactly, in obviously reduced subpulses of FSCS, and the sidelobes of spectrum can be effectively suppressed. Furthermore, aimed at the reconstructed spectrum, a new extraction method for microDoppler features of ballistic missile precession was proposed on the basis of dynamic planning, by using the smooth character of microDoppler curves. The effectiveness and robustness of the method was validated numerically.

The creditability of missile trajectory simulation model is not taken into a count based on the distributed environment of hardware-in-loop. From the view of engineering and practice, a strategy of self-adaptation of the simulation step size is designed and implemented in the real-time trajectory simulation. At the same time, two methods of missile trajectory simulation are presented according to the features of the distributed environment of hardware-in-loop: the simulation based on the environment of attacker and the simulation based on the environment of target aircraft. After analyzing the simulation results obtained from the two methods, the missile trajectory simulation based on the environment of target aircraft outperforms the one based on the environment of attacker. Undoubtedly, it has improved the creditability of real-time trajectory simulation in the hardware-in-loop environment to a great extent.

In order to provide an accurate mechanical environment of exterior ballistics for the safety and reliability design of fuze, a mathematical model of the motion of rotating projectile, which has dynamic unbalance angle and the axis of rotation of fuze being umparallel to the axis of projectile, around the center of mess in exterior ballistics is established based on the rigid body dynamics. The formulas of the axial, radial and tangential components of inertial force acting on fuze parts, which is caused by the motion of rotating projectile around the center of mess, are derived. The credibility of the theoretical analysis is verified by the simulation of ADAMS software. It can beknown from force analysis that, when the center of axial moving parts of fuze and the centroid of bullet and axis are on the same plane, and the distance between the centroid of axial moving parts of fuze and the inertia principal axis of projectile is maximum, the axial force and radial inertia force of fuze are greatly increased compared with the traditional calculation results (the inertia force of 155 mm caliber projectile achieves several times). The fuze axial moving partscan not be prevented frommoving forward under the action of axial force even if the radial and tangential forces are far greater than axial force in the condition of periodic fluctuation and large fluctuation amplitude. Key

An angular motion equation in complex form is established to study the angle of attack and velocity characteristics of spin-stabilized 2D trajectory correction projectile under the effect of fixed canards. The solution of forced motion when the canards spin at a constant rate and the analytical solutions of transient and steady state responses when the canards generate step excitation are both derived. The relationships between the amplitude and phase angle of average deflection angle and the parameters of the fixed canards are presented by deriving the analytical solutions of average velocity deflection angle. The flight stability conditions of spin stabilized 2D trajectory correction projectile under the effect of fixed canards are proposed. The result shows that the projectile should avoid resonance without control, and should limit the maximum increment of angle of attack and the equilibrium angle of attack with control. In addition, the phase angle of average deflection angle has a lead angle ahead of the roll angle of fixed canards. The results provide some references for the studies of flight stability and guidance method of spin-stabilized 2D trajectory correction projectile. Key

An underwater shooting experimental platform was built to research the evolutionary characteristics of muzzle flow field of ballistic gun during underwater submerged firing. The direct photography method was used to capture the whole evolution process of the flow field. The high-speed water column in front of bullet produces the water vapor at the muzzle before the bullet comes out of the bore; the under-expanded gas in the bore flows out after the bullet comes out of the bore, and blends with the water vaporto wrap around the bullet; after the bullet leaves from the muzzle, the gas jet continues to expand, and the head of jet is tapered; the surface of bullet is continuously cavitated to generate supercavitation, and at the same time, a slender air column is left at the tail of bullet. On the basis of experiment, a two-dimensional multi-phase flow model is established to simulate the experimental conditions, in which the fluid volume multiphase flow model, standard k-ε turbulence model, dynamic mesh and user-defined functions technology are used. The results indicate that a complex wave structure containing two bottle-shaped shock waves is formed after the highly under-expanded gunpowder gas exits from the muzzle during underwater submerged firing of ballisitc gun. After the bullet leaves from the muzzle, it accelerates continuously in the muzzle flow field. As the bullet moves away from the flow muzzle flow field, the velocity of bullet is continuously attenuated. Key

Based upon principles of solid propellant rocfcts and quasi-one dimen- tional flow theory, on the basis of interior ballistics a set of general purpose equations has been established. These equations can be used to calculate the interior ballistics of single chamber solid propellant rocket motors with long tail tubes or mnltiple propellant charges, or for motors with long tail tubes as well as mulitiple propellant charges. General pu- pose equations for calculating the equilibrium pressures have also been derived. Results of computation based on this method are in good agreement with experimental results.

In order to study the mutual interference between revolving bodies salvoed underwater in the water-exit process, the experimental research on the water-exit process of revolving bodies is carried out based on high-speed photography. The countors of cavity and revolving bodies are identified and extracted using image processing technology. The hydrodynamic disturbance between the revolving bodies in the water-exit process and the effect of frame velocity are analyzed by comparing the trajectory characteristics of single revolving body and two revolving bodies launched with and without submarine speed. The experimental results show that the low pressure zone formed by the first revolving body makes the cavity inside the second revolving body develops larger in the water-exit process without submarine speed, and the trajectoryof the second revolving body deflects to the first revolving body. The cavity evolution rule and the trajectory characteristics of revolving body change in the presence of submarine speed under the action of high pressure at the up-flow side and current scour, the cavity develops towards the back-flow side, and the trajectory of the first revolving body deflects along the flow direction; and the second revolving body is in the wake field of the first revolving body, so the trajectory of the second revolving body still has the attitude and the track deflection to the first revolving body, but its deflection amplitude is relatively smaller than that of the revolving body launched without submarine speed. Key