Experimental results indicate that propagation paths of cracks in geomaterials are often irregular. producing rough fracture surfaces which are fractal. A formula is derived for the fractal kinematics of crack propaga...Experimental results indicate that propagation paths of cracks in geomaterials are often irregular. producing rough fracture surfaces which are fractal. A formula is derived for the fractal kinematics of crack propagation in geomaterials. The formula correlates the dynamic and static fracture toughnesses with crack velocity, crack length and a microstructural parameter, and allows the fractal dimension to be obtained. From the equations for estimating crack velocity and fractal dimension it can be shown that the measured crack ve1ocity, Vo, should be much smaller than the fractal crack velocity, V. It can also be shown that the fractal dimension of the crack propagation path can be calculated directly from Vo and from the fracture toughness.展开更多
It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
This paper presents an analytical geometry method for kinematics and efficiency of planetary gear trains (PGTs). The novel method which is capable of evolution and contrast analysis of mechanism kinematics, can be app...This paper presents an analytical geometry method for kinematics and efficiency of planetary gear trains (PGTs). The novel method which is capable of evolution and contrast analysis of mechanism kinematics, can be applied to any typical one-and two-degree-of-freedom plane PGTs containing any number of simple, compound or complex-compound planetary gear sets. The efficiency analysis of this method features a systematized and programmed process and its independence of the speed ratio. The primary contribution of this work lies in the integration of quantitative calculation, qualitative evolution and comparative analysis of kinematics of PGTs into one diagram, and in the integration of kinematics and efficiency analysis into a single method system. First, the analytical geometry method is defined, its basic properties are given, and the systematization procedure to perform kinematic analysis is demonstrated. As an application, analytical geometry diagrams of common PGTs are exhibited in the form of a list, whose kinematic characteristics and general evolution tendency are discussed. Then, with the mapping of PGTs onto the angular speed plane, the efficiency formula of analytical geometry, which has an extremely concise form, and a simple method for power flow estimation are put forward. Moreover, a general procedure is provided to analyze the efficiency and power flow. Finally, four numerical examples including a complicated eleven-link differential PGTs are given to illustrate the simpleness and intuitiveness of the analytical geometry method.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
The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified.All geometries associated wit...The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified.All geometries associated with these realizations are also obtained by the contraction method.Further relations among the geometries are revealed.Most geometries fall into pairs.There exists t 1/(ν 2 t) correspondence in each pair.In the viewpoint of differential geometry,there are only 9 geometries,which have right signature and geometrical spatial isotropy.They are 3 relativistic geometries,3 absolute-time geometries,and 3 absolute-space geometries.展开更多
文摘Experimental results indicate that propagation paths of cracks in geomaterials are often irregular. producing rough fracture surfaces which are fractal. A formula is derived for the fractal kinematics of crack propagation in geomaterials. The formula correlates the dynamic and static fracture toughnesses with crack velocity, crack length and a microstructural parameter, and allows the fractal dimension to be obtained. From the equations for estimating crack velocity and fractal dimension it can be shown that the measured crack ve1ocity, Vo, should be much smaller than the fractal crack velocity, V. It can also be shown that the fractal dimension of the crack propagation path can be calculated directly from Vo and from the fracture toughness.
文摘It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
基金supported by the National Natural Science Foundation of China (Grant No. 51075407)the Fundamental Research Funds for the Central Universities (Grant No. CDJXS11111143)
文摘This paper presents an analytical geometry method for kinematics and efficiency of planetary gear trains (PGTs). The novel method which is capable of evolution and contrast analysis of mechanism kinematics, can be applied to any typical one-and two-degree-of-freedom plane PGTs containing any number of simple, compound or complex-compound planetary gear sets. The efficiency analysis of this method features a systematized and programmed process and its independence of the speed ratio. The primary contribution of this work lies in the integration of quantitative calculation, qualitative evolution and comparative analysis of kinematics of PGTs into one diagram, and in the integration of kinematics and efficiency analysis into a single method system. First, the analytical geometry method is defined, its basic properties are given, and the systematization procedure to perform kinematic analysis is demonstrated. As an application, analytical geometry diagrams of common PGTs are exhibited in the form of a list, whose kinematic characteristics and general evolution tendency are discussed. Then, with the mapping of PGTs onto the angular speed plane, the efficiency formula of analytical geometry, which has an extremely concise form, and a simple method for power flow estimation are put forward. Moreover, a general procedure is provided to analyze the efficiency and power flow. Finally, four numerical examples including a complicated eleven-link differential PGTs are given to illustrate the simpleness and intuitiveness of the analytical geometry method.
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supported by the National Natural Science Foundation of China (Grant Nos. 10775140,10975141,10705048,10731080,10975141,11175245 and 11075206)the Fundamental Research Funds for the Central Universities (Grant No. 105116)
文摘The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified.All geometries associated with these realizations are also obtained by the contraction method.Further relations among the geometries are revealed.Most geometries fall into pairs.There exists t 1/(ν 2 t) correspondence in each pair.In the viewpoint of differential geometry,there are only 9 geometries,which have right signature and geometrical spatial isotropy.They are 3 relativistic geometries,3 absolute-time geometries,and 3 absolute-space geometries.
