This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the...This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the Pfaff action of rotating relativistic Birkhoffian systems was defined. The Pfaff-Birkhoff principles and Birkhoff＇s equations of the constrained rotating relativistic systems were obtained. The geometrical description, the exact properties and their forms on R T^＊M for the constrained rotating relativistic Birkhoffian systems are given. The global analyses of the autonomous, semi-autonomous and non-autonomous constrained relativistic Birkhoff＇s equations as well as the geometrical properties of energy change for the constrained rotating relativistic Birkhoffian systems were also conducted.展开更多
This article, firstly, categorizes aircraft＇s presented area in a particular hit aspect into non-vulnerable region, non-overlapping vulnerable region and overlapping vulnerable region. Then, the aircraft＇s unique ex...This article, firstly, categorizes aircraft＇s presented area in a particular hit aspect into non-vulnerable region, non-overlapping vulnerable region and overlapping vulnerable region. Then, the aircraft＇s unique existing states are divided into kill states, intermediate states and no kill states. The parameters pertinent to aircraft＇s existing states in the above-mentioned regions are analyzed by using the shot line scanning method. Finally, the method provides two kinds of shot line geometric descriptive data： （1） component＇s vulnerable area and presented area in each region, which can be used to calculate the component＇s single-hit vulnerability and （2） aircraft＇s unique existing states and the areas corresponding to each state, which can be used to calculate the aircraft＇s single-hit and multi-hit vulnerability. Examples show that the proposed method can provide the parameters of the aircraft＇s or its component＇s area under threat being hit through tracing the shot line path thereby enabling the vulnerability calculated results to conform with reality to larger extent. In addition, the method solves the generality problem in dealing with overlapping components.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos.10672143, 10372053）, and the Natural Science Foundation of Henan Province （Grant Nos.03011011400, 05011022200）
文摘This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the Pfaff action of rotating relativistic Birkhoffian systems was defined. The Pfaff-Birkhoff principles and Birkhoff＇s equations of the constrained rotating relativistic systems were obtained. The geometrical description, the exact properties and their forms on R T^＊M for the constrained rotating relativistic Birkhoffian systems are given. The global analyses of the autonomous, semi-autonomous and non-autonomous constrained relativistic Birkhoff＇s equations as well as the geometrical properties of energy change for the constrained rotating relativistic Birkhoffian systems were also conducted.
基金Foundation items： Ph.D. Programs Foundation of Ministry of Education of China （200806991002） Natural Science Foundation of Shaanxi Province （SJ08A 11）+1 种基金 NPU Foundation for Fundamental Research （NPU-FFR JC200804） NPU Young Teacher Foundation （W016208）
文摘This article, firstly, categorizes aircraft＇s presented area in a particular hit aspect into non-vulnerable region, non-overlapping vulnerable region and overlapping vulnerable region. Then, the aircraft＇s unique existing states are divided into kill states, intermediate states and no kill states. The parameters pertinent to aircraft＇s existing states in the above-mentioned regions are analyzed by using the shot line scanning method. Finally, the method provides two kinds of shot line geometric descriptive data： （1） component＇s vulnerable area and presented area in each region, which can be used to calculate the component＇s single-hit vulnerability and （2） aircraft＇s unique existing states and the areas corresponding to each state, which can be used to calculate the aircraft＇s single-hit and multi-hit vulnerability. Examples show that the proposed method can provide the parameters of the aircraft＇s or its component＇s area under threat being hit through tracing the shot line path thereby enabling the vulnerability calculated results to conform with reality to larger extent. In addition, the method solves the generality problem in dealing with overlapping components.
