The rotation of skew bridges in the plane is a common phenomenon in engineering. Traditional measure is to setup pins or limiting displacement with lateral bearings, but the result is not satisfactory. In order to sol...The rotation of skew bridges in the plane is a common phenomenon in engineering. Traditional measure is to setup pins or limiting displacement with lateral bearings, but the result is not satisfactory. In order to solve this problem, the reason for the rotation in the plane is found by philosophy analysis and an idea regarding the application of slantleg frame skew bridges without abutment is brought forward in this paper. Theory and engineering practices indicate that slant-leg rigid frame bridges without abutment can restrain the rotation of skew bridges in the plane to the utmost extent because of its structural characteristics and can fundamentally solve the tough defect of skew bridges.展开更多
Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein-Gordon/Fermi Pasta-Ulam diatomic chain using the expanded rotating plane-wave approxi...Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein-Gordon/Fermi Pasta-Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.展开更多
It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new mo...It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper,based on the classical differential geometry curve theory.Firstly,the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS,the kinematic equations of LOS are established,and the concepts of curvature and torsion of LOS are proposed.Simultaneously,the new relative dynamic equations between interceptor and target are constructed.Secondly,it is found that there is an instan-taneous rotation plane of LOS (IRPL) in the space,in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems.The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN.In addition,the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL.After that,the dif-ferential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced,and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC.Moreover,the performance of the original guidance laws will be reduced after the differential geometric transformation.At last,an exoatmospheric intercep-tion is taken for simulation to demonstrate the differential geometric modeling proposed in this paper.展开更多
Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional n...Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation （TPN）, no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.展开更多
文摘The rotation of skew bridges in the plane is a common phenomenon in engineering. Traditional measure is to setup pins or limiting displacement with lateral bearings, but the result is not satisfactory. In order to solve this problem, the reason for the rotation in the plane is found by philosophy analysis and an idea regarding the application of slantleg frame skew bridges without abutment is brought forward in this paper. Theory and engineering practices indicate that slant-leg rigid frame bridges without abutment can restrain the rotation of skew bridges in the plane to the utmost extent because of its structural characteristics and can fundamentally solve the tough defect of skew bridges.
基金Project supported by the National Natural Science Foundation of China (Grant No.10574011)the Foundation for Innovative Research Groups Foundation of Beijing Normal University
文摘Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein-Gordon/Fermi Pasta-Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.
文摘It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper,based on the classical differential geometry curve theory.Firstly,the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS,the kinematic equations of LOS are established,and the concepts of curvature and torsion of LOS are proposed.Simultaneously,the new relative dynamic equations between interceptor and target are constructed.Secondly,it is found that there is an instan-taneous rotation plane of LOS (IRPL) in the space,in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems.The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN.In addition,the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL.After that,the dif-ferential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced,and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC.Moreover,the performance of the original guidance laws will be reduced after the differential geometric transformation.At last,an exoatmospheric intercep-tion is taken for simulation to demonstrate the differential geometric modeling proposed in this paper.
基金co-supported by the National Science Foundation of China(No.11222215)the National Basic Research Program of China(No.2013CB733100)
文摘Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation （TPN）, no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.
