When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ...When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.展开更多
There exists a property “structural stability” for “4-dimensional canards” which is a singular-limit solution in a slow-fast system with a bifurcation parameter. It means that the system includes the possibility t...There exists a property “structural stability” for “4-dimensional canards” which is a singular-limit solution in a slow-fast system with a bifurcation parameter. It means that the system includes the possibility to have some critical values on the bifurcation parameter. Corresponding to these values, the pseudo-singular point, which is a singular point in the time-scaled-reduced system should be changed to another one. Then, the canards may fly to another pseudo-singular point, if possible. Can the canards fly? The structural stability gives the possibility for the canards flying. The precise reasons why happen are described in this paper.展开更多
Existing literature has shown that the control force at the nose could cause dynamic instability for controlled projectiles. To lower the adverse impact on the dual-spin projectile with fixed canards under the premise...Existing literature has shown that the control force at the nose could cause dynamic instability for controlled projectiles. To lower the adverse impact on the dual-spin projectile with fixed canards under the premise of meeting guidance system requirements, the influence of control moment provided by a motor on the flight stability is analyzed in this paper. Firstly, the effect of the rolling movement on stability is analyzed based on the stability criterion derived using the Hurwitz stability theory. Secondly, the evaluation parameters combining the features of different control periods that could assess the variation of stability features after the motor torque are obtained. These effective formulas are used to indicate that, to reduce the flight instability risks, the stabilized rolling speed of roll speed keeping period should be as small as possible; the variation trend of motor torque during the rolling speed controlling period and the roll angle of the forward body during roll angle switching period are recommended corresponding to the projectile and trajectory characteristics. Moreover,detailed numerical simulations of 155 mm dual-spin projectile are satisfactory agreement with the theoretical results.展开更多
The purpose of increasing the aerodynamic efficiency and enhancing the supermaneuverability for the selected supersonic aircraft is presented. Aerodynamic characteristics, the surface pressure distribution and the max...The purpose of increasing the aerodynamic efficiency and enhancing the supermaneuverability for the selected supersonic aircraft is presented. Aerodynamic characteristics, the surface pressure distribution and the maximum lift are estimated for the baseline configuration for different Mach numbers and attack angles in subson- ic and supersonic potential flows, using a low-order three-dimensional panel method supported with the semi-empirical formulas of the data compendium （DATCOM）. Total nose-up and nose-down pitching moments about the center of gravity of the complete aircraft in the subsonic region depending on flight conditions and aircraft performance limitations are estimated. A software package is developed to implement the two-dimensional thrust vectoring flight control technique （pitch vectoring up and down） controlled by the advanced aerodynamic and control surface （the foreplane or the canard）. Results show that the canard with the thrust vectoring produces enough nose-down moment and can support the stabilizer at high maneuvers. The suggested surface can increase the aerodynamic efficiency （lift-to-drag ratio） of the baseline configuration by 5%-6% in subsonic and supersonic flight regimes.展开更多
To study the rolling control characteristics of a canard-controlled missile, a series of wind tunnel experiment is conducted. The experimental method, the structure features of wind tunnel model and the experimental r...To study the rolling control characteristics of a canard-controlled missile, a series of wind tunnel experiment is conducted. The experimental method, the structure features of wind tunnel model and the experimental results are introduced in this paper. The experimental data show that the canard is an inefficient rolling control device for canard-controlled missile with fixed tail fins; but for the free-spinning tail fin configuration, the canard can conduct rolling control of the missile, and even have higher controlling efficiency under larger canard deflection angle.展开更多
The steady flow field of a canard missile on different angles of attack and Mach numbers were studied. Based on analysis, a method was proposed to reduce the calculation for the rolling characteristics of the canard m...The steady flow field of a canard missile on different angles of attack and Mach numbers were studied. Based on analysis, a method was proposed to reduce the calculation for the rolling characteristics of the canard missile with free-spinning tails, and was tested to obtain the relations between rolling moment coefficient, Mach number, and angle of attack. All the computed rolling moment coefficients obtained from the proposed method greatly agreed with the experimental results of FD-06 wind tunnel in CAAA, which proved that the method can not only reduce the calculation cost but also keep precision in calculating the rolling characteristics of canard missiles.展开更多
This paper reports on the canard phenomenon occurring in a rheodynamic model of cardiac pressure pulsations. By singular perturbation techniques the corresponding parameter value at which canards exist is obtained. Th...This paper reports on the canard phenomenon occurring in a rheodynamic model of cardiac pressure pulsations. By singular perturbation techniques the corresponding parameter value at which canards exist is obtained. The physiological significance of canards in this model is given.展开更多
In this article, the interference between canard and wing is discussed on the basis of wind-tunnel test, with a brief review of the development of aerodynamic configurations of AD-100 / 200 (two light canard aircraft ...In this article, the interference between canard and wing is discussed on the basis of wind-tunnel test, with a brief review of the development of aerodynamic configurations of AD-100 / 200 (two light canard aircraft designed by NAI) .The safety against stall of a canard is also discussed based upon flight test.The rule 'canard stall first'is introduced as an effective measure to improve safety against stall. It has been pointed out that the rule may threaten the flight safety at low-altitude. Finally,what a designer can do to remove the threat is presented.展开更多
The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the syst...The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the system has a unique limit cycle, homoclinic orbits, canards or the unique equilibrium point is globally asymptotic stable are given. The methods in our previous papers are used for the proofs.展开更多
The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only...The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only yields a steady state. Also,. the performance of such oscillations shows two maxima with the variation of the system size, indicating the occurrence of system size resonance. This behavior is found to be intimately connected with the canard phenomenon. Interestingly, it is also found that one of the optimal system sizes matches well with the real cell size, and such a match is robust to the variation of the control parameters.展开更多
Let us consider higher dimensional canards in a sow-fast system R<sup>2+2</sup> with a bifurcation parameter. Then, the slow manifold sometimes shows various aspects due to the bifurcation. Introducing a k...Let us consider higher dimensional canards in a sow-fast system R<sup>2+2</sup> with a bifurcation parameter. Then, the slow manifold sometimes shows various aspects due to the bifurcation. Introducing a key notion “symmetry” to the slow-fast system, it becomes clear when the pseudo singular point obtains the structural stability or not. It should be treated with a general case. Then, it will also be given about the sufficient conditions for the existence of the center manifold under being “symmetry”. The higher dimensional canards in the sow-fast system are deeply related to Hilbert’s 16th problem. Furthermore, computer simulations are done for the systems having Brownian motions. As a result, the rigidity for the system is confirmed.展开更多
The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as...The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.展开更多
The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing （Canard-FSW） configurations is simulated numerically by employing the numerical wind tunnel ...The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing （Canard-FSW） configurations is simulated numerically by employing the numerical wind tunnel method. The variations of aerodynamic characteristics of Canard-FSW configurations with different positions of the canard are investigated,finding that the aerodynamic interference and mutual coupling effect between the canard and main wing have made great contributions to the lift and stability characteristics of the whole aircraft. Canard can radically improve the surface flow pattern of the main wing. And its own vortex can have a favorable interference on the main wing and can effectively control the airflow boundary layer separation. At small angles of attack,the aerodynamic characteristics are sensitive to the positions of the canard and the main wing,but at high angles of attack,the aerodynamic performances of the configuration are not only related to the shape of the canard （forward or backward）,but also with the size of control force as well as the features of the vortices generated above the main wing and the canard. The different configurations and vortices are illustrated using the velocity vector,streamlines and pressure contours.展开更多
The fixed canards configuration of a dual-spin projectile makes it difficult to apply the traditional guidance law. In this study, a modified impact point prediction guidance strategy based on an iterative process was...The fixed canards configuration of a dual-spin projectile makes it difficult to apply the traditional guidance law. In this study, a modified impact point prediction guidance strategy based on an iterative process was developed for a class of dual-spin projectiles with fixed canards, to reduce the impact point dispersion. The guidance strategy is dependent on the modified projectile linear theory to rapidly predict the flight states and the impact point. For projectiles with control applied to the trajectory, the modified projectile linear theory method is known to achieve poor impact point prediction. To improve the prediction accuracy, improvements were made to the modified projectile linear theory by considering the products of the yaw rate and other small quantities.The guidance strategy is based on the iterative process for the continuous adjustment of the expected output of the roll angle of the course correction fuze, to minimize the direction error between the predicted impact point and target location. Studies were conducted on a model dual-spin projectile configuration to demonstrate the guidance details. The numerical simulations indicate that the proposed guidance strategy can effectively reduce the projectile impact point dispersion.展开更多
文摘When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.
文摘There exists a property “structural stability” for “4-dimensional canards” which is a singular-limit solution in a slow-fast system with a bifurcation parameter. It means that the system includes the possibility to have some critical values on the bifurcation parameter. Corresponding to these values, the pseudo-singular point, which is a singular point in the time-scaled-reduced system should be changed to another one. Then, the canards may fly to another pseudo-singular point, if possible. Can the canards fly? The structural stability gives the possibility for the canards flying. The precise reasons why happen are described in this paper.
文摘Existing literature has shown that the control force at the nose could cause dynamic instability for controlled projectiles. To lower the adverse impact on the dual-spin projectile with fixed canards under the premise of meeting guidance system requirements, the influence of control moment provided by a motor on the flight stability is analyzed in this paper. Firstly, the effect of the rolling movement on stability is analyzed based on the stability criterion derived using the Hurwitz stability theory. Secondly, the evaluation parameters combining the features of different control periods that could assess the variation of stability features after the motor torque are obtained. These effective formulas are used to indicate that, to reduce the flight instability risks, the stabilized rolling speed of roll speed keeping period should be as small as possible; the variation trend of motor torque during the rolling speed controlling period and the roll angle of the forward body during roll angle switching period are recommended corresponding to the projectile and trajectory characteristics. Moreover,detailed numerical simulations of 155 mm dual-spin projectile are satisfactory agreement with the theoretical results.
文摘The purpose of increasing the aerodynamic efficiency and enhancing the supermaneuverability for the selected supersonic aircraft is presented. Aerodynamic characteristics, the surface pressure distribution and the maximum lift are estimated for the baseline configuration for different Mach numbers and attack angles in subson- ic and supersonic potential flows, using a low-order three-dimensional panel method supported with the semi-empirical formulas of the data compendium （DATCOM）. Total nose-up and nose-down pitching moments about the center of gravity of the complete aircraft in the subsonic region depending on flight conditions and aircraft performance limitations are estimated. A software package is developed to implement the two-dimensional thrust vectoring flight control technique （pitch vectoring up and down） controlled by the advanced aerodynamic and control surface （the foreplane or the canard）. Results show that the canard with the thrust vectoring produces enough nose-down moment and can support the stabilizer at high maneuvers. The suggested surface can increase the aerodynamic efficiency （lift-to-drag ratio） of the baseline configuration by 5%-6% in subsonic and supersonic flight regimes.
文摘To study the rolling control characteristics of a canard-controlled missile, a series of wind tunnel experiment is conducted. The experimental method, the structure features of wind tunnel model and the experimental results are introduced in this paper. The experimental data show that the canard is an inefficient rolling control device for canard-controlled missile with fixed tail fins; but for the free-spinning tail fin configuration, the canard can conduct rolling control of the missile, and even have higher controlling efficiency under larger canard deflection angle.
基金Sponsored by the Fundamental Research Funds for the Central Universities(Grant No.HEUCFG201815)
文摘The steady flow field of a canard missile on different angles of attack and Mach numbers were studied. Based on analysis, a method was proposed to reduce the calculation for the rolling characteristics of the canard missile with free-spinning tails, and was tested to obtain the relations between rolling moment coefficient, Mach number, and angle of attack. All the computed rolling moment coefficients obtained from the proposed method greatly agreed with the experimental results of FD-06 wind tunnel in CAAA, which proved that the method can not only reduce the calculation cost but also keep precision in calculating the rolling characteristics of canard missiles.
文摘This paper reports on the canard phenomenon occurring in a rheodynamic model of cardiac pressure pulsations. By singular perturbation techniques the corresponding parameter value at which canards exist is obtained. The physiological significance of canards in this model is given.
文摘In this article, the interference between canard and wing is discussed on the basis of wind-tunnel test, with a brief review of the development of aerodynamic configurations of AD-100 / 200 (two light canard aircraft designed by NAI) .The safety against stall of a canard is also discussed based upon flight test.The rule 'canard stall first'is introduced as an effective measure to improve safety against stall. It has been pointed out that the rule may threaten the flight safety at low-altitude. Finally,what a designer can do to remove the threat is presented.
文摘The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the system has a unique limit cycle, homoclinic orbits, canards or the unique equilibrium point is globally asymptotic stable are given. The methods in our previous papers are used for the proofs.
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.20433050 and No.20673106）.
文摘The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only yields a steady state. Also,. the performance of such oscillations shows two maxima with the variation of the system size, indicating the occurrence of system size resonance. This behavior is found to be intimately connected with the canard phenomenon. Interestingly, it is also found that one of the optimal system sizes matches well with the real cell size, and such a match is robust to the variation of the control parameters.
文摘Let us consider higher dimensional canards in a sow-fast system R<sup>2+2</sup> with a bifurcation parameter. Then, the slow manifold sometimes shows various aspects due to the bifurcation. Introducing a key notion “symmetry” to the slow-fast system, it becomes clear when the pseudo singular point obtains the structural stability or not. It should be treated with a general case. Then, it will also be given about the sufficient conditions for the existence of the center manifold under being “symmetry”. The higher dimensional canards in the sow-fast system are deeply related to Hilbert’s 16th problem. Furthermore, computer simulations are done for the systems having Brownian motions. As a result, the rigidity for the system is confirmed.
文摘The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.
基金National Defense Basic Research Program (B222006060)
文摘The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing （Canard-FSW） configurations is simulated numerically by employing the numerical wind tunnel method. The variations of aerodynamic characteristics of Canard-FSW configurations with different positions of the canard are investigated,finding that the aerodynamic interference and mutual coupling effect between the canard and main wing have made great contributions to the lift and stability characteristics of the whole aircraft. Canard can radically improve the surface flow pattern of the main wing. And its own vortex can have a favorable interference on the main wing and can effectively control the airflow boundary layer separation. At small angles of attack,the aerodynamic characteristics are sensitive to the positions of the canard and the main wing,but at high angles of attack,the aerodynamic performances of the configuration are not only related to the shape of the canard （forward or backward）,but also with the size of control force as well as the features of the vortices generated above the main wing and the canard. The different configurations and vortices are illustrated using the velocity vector,streamlines and pressure contours.
文摘The fixed canards configuration of a dual-spin projectile makes it difficult to apply the traditional guidance law. In this study, a modified impact point prediction guidance strategy based on an iterative process was developed for a class of dual-spin projectiles with fixed canards, to reduce the impact point dispersion. The guidance strategy is dependent on the modified projectile linear theory to rapidly predict the flight states and the impact point. For projectiles with control applied to the trajectory, the modified projectile linear theory method is known to achieve poor impact point prediction. To improve the prediction accuracy, improvements were made to the modified projectile linear theory by considering the products of the yaw rate and other small quantities.The guidance strategy is based on the iterative process for the continuous adjustment of the expected output of the roll angle of the course correction fuze, to minimize the direction error between the predicted impact point and target location. Studies were conducted on a model dual-spin projectile configuration to demonstrate the guidance details. The numerical simulations indicate that the proposed guidance strategy can effectively reduce the projectile impact point dispersion.
