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PARAMETRIC EQUATIONS OF NONHOLONOMIC NONCONSERVATIVE SYSTEMS IN THE EVENT SPACE AND THE METHOD OF THEIR INTEGRATION 被引量:10
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作者 Mei Fengxiang (Beijing Institute of Technology) 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1990年第2期160-168,共9页
In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then th... In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given. 展开更多
关键词 event space nonholonomic nonconservative system parametric equation integration method
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Poisson theory and integration method of Birkhoffian systems in the event space 被引量:6
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作者 张毅 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第8期80-84,共5页
This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian sy... This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by (2n + 1) Birkhoff's variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results. 展开更多
关键词 Birkhoffian system event space method of integration Jacobi last multiplier
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Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space 被引量:5
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作者 张毅 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第11期4636-4642,共7页
This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding confor... This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results. 展开更多
关键词 holonomic system conformal invariance SYMMETRY event space
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Integrating Factors and Conservation Laws of Generalized Birkhoff System Dynamics in Event Space 被引量:5
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作者 ZHANG Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第6期1078-1082,共5页
In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff... In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results. 展开更多
关键词 generalized Birkhoff system dynamics conservation law event space integrating tactor
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Conformal Invariance and Noether Symmetry, Lie Symmetry of Birkhoffian Systems in Event Space 被引量:4
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作者 张毅 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第1期166-170,共5页
This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigati... This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results. 展开更多
关键词 Birkhoffian system event space conformal invariance Noether symmetry Lie symmetry
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Routh method of reduction for Birkhoffian systems in the event space 被引量:1
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作者 张毅 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第12期4365-4368,共4页
For a Birkhoffian system in the event space, this paper presents the Routh method of reduction. The parametric equations of the Birkhoffian system in the event space are established, and the definition of cyclic coord... For a Birkhoffian system in the event space, this paper presents the Routh method of reduction. The parametric equations of the Birkhoffian system in the event space are established, and the definition of cyclic coordinates for the system is given and the corresponding cyclic integral is obtained. Through the cyclic integral, the order of the system can be reduced. The Routh functions for the Birkhoffian system in the event space are constructed, and the Routh method of reduction is successfully generalized to the Birkhoffian system in the event space. The results show that if the system has a cyclic integral, then the parametric equations of the system can be reduced at least by two degrees and the form of the equations holds. An example is given to illustrate the application of the results. 展开更多
关键词 event space Birkhoffian system REDUCTION cyclic integral
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A General Approach to the Construction of Conservation Laws for Birkhoffian Systems in Event Space 被引量:1
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作者 ZHANG Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期851-854,共4页
For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the paramet... For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results. 展开更多
关键词 event space Birkhoffian system integrating factor conservation theorem Killing equation
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NOETHER'S THEOREM FOR NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS IN EVENT SPACE 被引量:1
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作者 李元成 张毅 梁景辉 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第5期543-548,共6页
To study the Noether's theorem of nonholonomic systems of non_Chetaev's type with unilateral constraints in event space, firstly, the principle of D'Alembert_Lagrange for the systems with unilateral constr... To study the Noether's theorem of nonholonomic systems of non_Chetaev's type with unilateral constraints in event space, firstly, the principle of D'Alembert_Lagrange for the systems with unilateral constraints in event space is presented, secondly, the Noether's theorem and the Noether's inverse theorem for the nonholonomic systems of non_Chetaev's type with unilateral constraints in event space are studied and obtained, which is based upon the invariance of the differential variational principle under the infinitesimal transformations of group, finally, an example is given to illustrate the application of the result. 展开更多
关键词 analytical mechanics event space unilateral constraint nonholonomic system Noether's theorem Noeter's inverse theorem
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Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space 被引量:1
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作者 贾利群 张耀宇 罗绍凯 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第11期3168-3175,共8页
Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetacv type in the event space are investigated. The dif... Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetacv type in the event space are investigated. The differential equations of motion of the system above are established. The criteria of the Lie symmetry, the Noether symmetry and the form invariance are given and the relations between them are obtained. The Hojman conserved quantities are gained by which the Hojman theorem is extended and applied to the nonholonomic system of the unilateral non-Chetacv type in the event space. An example is given to illustrate the application of the results. 展开更多
关键词 event space unilateral nonholonomic system Hojman conserved quantity
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Unified Symmetry of Nonholonomic System of Non-Chetaev's Type in Event Space
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作者 HOU Qi-Bao LI Yuan-Cheng WANG Jing XIA Li-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2期221-224,共4页
The unified symmetry of a nonholonomic system of non-Chetaev's type in event space under infinitesimal transformations of group is studied. Firstly, the differential equations of motion of the system are given. Secon... The unified symmetry of a nonholonomic system of non-Chetaev's type in event space under infinitesimal transformations of group is studied. Firstly, the differential equations of motion of the system are given. Secondly, the definition and the criterion of the unified symmetry for the system are obtained. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev's type. Finally, an example is given to illustrate the application of the result. 展开更多
关键词 event space nonholonomic system unified symmetry conserved quantity
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Unified symmetry of the nonholonomic system of non-Chetaev type with unilateral constraints in event space
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作者 后其宝 李元成 +1 位作者 王静 夏丽莉 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第6期1521-1525,共5页
This paper studies the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints in event space under infinitesimal transformations of group. Firstly, it gives the differential equation... This paper studies the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints in event space under infinitesimal transformations of group. Firstly, it gives the differential equations of motion of the system. Secondly, it obtains the definition and the criterion of the unified symmetry for the system. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints. Finally, an example is given to illustrate the application of the results. 展开更多
关键词 event space unilateral constraint unified symmetry conserved quantity
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Hojman Conserved Quantities for Birkhoffian Systems in Event Space
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作者 ZHANG Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第7期59-62,共4页
This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry fora Birkhoffian system in the event space.The Birkhoffian parametric equations for the system are established,and thedet... This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry fora Birkhoffian system in the event space.The Birkhoffian parametric equations for the system are established,and thedetermining equations of Lie symmetry for the system are obtained.The conditions under which a Lie symmetry ofBirkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojmanconserved quantity are given.An example is given to illustrate the application of the results. 展开更多
关键词 event space Birkhoffian system Lie symmetry Hojman conserved quantity
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Lie-Form Invariance of the Nonholonomic System of Relative Motion in Event Space
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作者 HOU Qi-Bao LI Yuan-Cheng WANG Jing XIA Li-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第5X期795-798,共4页
In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative... In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results. 展开更多
关键词 event space nonholonomic system relative motion Lie-form invariance conserved quantity
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THE CONSERVATION LAW OF NONHOLONOMIC SYSTEM OF SECOND-ORDER NON-CHETAVE'S TYPE IN EVENT SPACE
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作者 FANG Jian-hui(方建会) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第1期89-94,共6页
The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's prin... The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given. 展开更多
关键词 event space Jourdain's principle nonholonomic system conservation law
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Unified Symmetry of Nonholonomic System of Non-Chetaev's Type with Variable Mass in Event Space
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作者 HOU Qi-Bao LI Yuan-Cheng XiA Li-Li WANG Jing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第4X期619-622,共4页
The unified symmetry of a nonholonomic system of non-Chetaev's type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and the criterion of... The unified symmetry of a nonholonomic system of non-Chetaev's type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and the criterion of the unified symmetry for the system are obtained. Finally, the Noether conserved quantity, the Hojman conserved quantity, and a new type of conserved quantity are deduced from the unified symmetry of the nonholonomic system of non-Chetaev's type with variable mass in event space at one time. An example is given to illustrate the application of the results. 展开更多
关键词 event space nonholonomic system variable mass unified symmetry conserved quantity
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Symmetry of the Lagrangians of holonomic nonconservative system in event space
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作者 张斌 方建会 张伟伟 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第7期61-65,共5页
This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quan... This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result at the end. 展开更多
关键词 symmetry of Lagrangians event space holonomic nonconservative system conservedquantity
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Combined Gradient Representations for Generalized Birkhoffian Systems in Event Space and Its Stability Analysis
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作者 WANG Jiahang BAO Siyuan 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2021年第6期967-974,共8页
The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given... The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results. 展开更多
关键词 generalized Birkhoffian system event space combined gradient systems stability
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Higher-order differential variational principle and differential equations of motion for mechanical systems in event space
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作者 张相武 李院院 +1 位作者 赵小侠 罗文峰 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第10期292-298,共7页
In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the... In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained. 展开更多
关键词 event space the higher-order d'Alembert-Lagrange principle the higher-order time rate of changeof force the higher-order differential equations of motion
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Riemann Hypothesis, Catholic Information and Potential of Events with New Techniques for Financial and Other Applications
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作者 Prodromos Char. Papadopoulos 《Advances in Pure Mathematics》 2021年第5期524-572,共49页
In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic... In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions (<img src="Edit_5f13a4a5-abc6-4bc5-9e4c-4ff981627b2a.png" width="33" height="21" alt="" />) which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function <em>ζ</em>(<em>s</em>) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9. 展开更多
关键词 Twin Problem Twin’s Problem Unsolved Mathematical Problems Prime Number Problems Millennium Problems Riemann Hypothesis Riemann’s Hypothesis Number Theory Information Theory Probabilities Statistics Management Financial Applications Arithmetical Analysis Optimization Theory Stock Exchange Mathematics Approximation Methods Manifolds Economical Mathematics Random Variables space of events Strategy Games Probability Density Stock Market Technical Analysis Forecasting
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Model of constant probability event and its application in information fusion
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作者 邓勇 施文康 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2004年第1期25-30,共6页
A model of constant probability event is constructed rigorously in event space of PSCEA. It is showed that the numericalbased fusion and the algebraicbased fusion have a consistent result when the weight is regarded a... A model of constant probability event is constructed rigorously in event space of PSCEA. It is showed that the numericalbased fusion and the algebraicbased fusion have a consistent result when the weight is regarded as a constant probability event. From the point of view of algebra, we present a novel similarity measure in product space. Based on the similarity degree, we use a similarity aggregation method to fusion experts' evaluation. We also give a numerical example to illustrate the method. 展开更多
关键词 product space conditional event algebra constant probability event similarity measure
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