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ON THE integrating factor OF ABEL EQUATION

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Annals of Differential Equations 1995年第1期11卷 114-116页

作者：应益荣党新益西安西北大学

The necessary and sufficient condition of a sort of rational faction integrating factor of Abel equation is derived from this paper.

关键词： Abel equation integrating factor

integrating factors and Conservation Laws for Relativistic Mechanical System

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Communications in Theoretical Physics 2005年第2X期44卷 231-234页

作者： ZHANG Yi Department of Civil Engineering University of Science and Technology of Suzhou Suzhou 215011 China

In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems 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 systems are established, and an example is given to illustrate the application of the results.

关键词： relativity mechanical system conservation law integrating factor Killing equation

integrating factors and Conservation Theorems for the Nonholonomic Singular Lagrange System

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Communications in Theoretical Physics 2007年第5X期48卷 791-794页

作者： ZHAO Shu-Hong LIANG Li-Fu QIAO Yong-Fen School of Civil Engineering of Harbin Engineering University Harbin 150001 China Engineering College of Northeast Agricultural University Harbin 150030 China

We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.

关键词： analytical mechanics singular system integrating factor conserved quantity

integrating factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

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Communications in Theoretical Physics 2006年第1X期46卷 43-45页

作者： QIAO Yong-Fen ZHAO Shu-Hong Department of Mechanical Engineering and Automation Zhejiang Science and Technology University Hangzhou 310018 China Engineering College of Northeast Agricultural University Harbin 150030 China

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.

关键词： generalized nonconservative system Lagrangian equation conservation theorem integrating factor

integrating factors and Conservation Theorems of Nonholonomic Dynamical System of Relative Motion

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Communications in Theoretical Physics 2007年第2期47卷 217-220页

作者： QIAO Yong-Fen ZHAO Shu-Hong LI Ren-Jie Engineering College of Northeast Agricultural University Harbin 150030 China Faculty of Science Laiyang Agricultural College Laiyang. 265200 China

The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.

关键词： nonholonomic system relative motion integrating factor conservation theorem

integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

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Chinese Physics B 2002年第8期11卷 760-764页

作者：李仁杰刘洋等 EegineeringCollegeofNortheastAgricultrueUniversity Harbin150003China CivilEngineeringCollgegofHarbinEngineeringUniversity Harbin150001China

We present a general approach to the construction of conservation laws for variable mass nonholonomic noncon-servative systems. First, we give the definition of integrating factors, and we study in detail the necessary conditionsfor the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem forHamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally,we give an example to illustrate the application of the results.

关键词： variable mass nonholonomic nonconservative system Hamilton's canonical equations integrating factor conservation law

integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics

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Chinese Physics B 2002年第10期11卷 988-992页

作者：乔永芬张耀良等 EngineeringCollegeofNortheastAgricultureUniversity Harbin150030China DepartmentofCivilEngineering HarbinEngineeringUniversityHarbin150001China

In this paper, we present a general approach to the construction of conservation laws for generalized classical dynamical systems. Firstly, we give the definition of integrating factors and, secondly, we study in detail the necessary conditions for the existence of conserved quantities. Then we establish the conservation theorem and its inverse for the Hamilton's canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics. Finally, we give an example to illustrate the application of the results.

关键词： generalized classical mechanics holonomic nonconservative system Hamilton's canonical equation integrating factor conservation theorem

Solution of Center-Focus Problem for a Class of Cubic Systems

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Chinese Annals of Mathematics,Series B 2016年第1期37卷 149-160页

作者： Bo SANG Chuanze NIU School of Mathematical Sciences Liaocheng University

For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin.

关键词： Center variety Isochronous center Center conditions integrating factor

Investigation of new solutions for an extended(2+1)-dimensional Calogero-Bogoyavlenskii-Schif equation

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Frontiers of Mathematics in China 2021年第4期16卷 925-936页

作者： Mohamed R.ALI R.SADAT Wen-Xiu MA Department of Mathematics Faculty of EngineeringBenha UniversityEgypt Department of Mathematics Zagazig Faculty of EngineeringZagazig UniversityZagazigEgypt Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL33620-5700USA School of Mathematics South China University of TechnologyGuangzhou 510640China School of Mathematical and Statistical Sciences North-West UniversityMafikeng CamusPrivate Bag X2046Mmabatho 2735South Africa

We investigate and concentrate on new infinitesimal generators of Lie symmetries for an extended(2+1)-dimensional Calogero-Bogoyavlenskii-Schif(eCBS)equation using the commutator table which results in a system of nonlinear ordinary differential equations(ODEs)which can be manually *** two stages of Lie symmetry reductions,the eCBS equation is reduced to non-solvable nonlinear ODEs using different combinations of optimal Lie *** the integration method and the Riccati and Bernoulli equation methods,we investigate new analytical solutions to those *** substituting to the original variables generates new solutions to the eCBS *** results are simulated through three-and two-dimensional plots.

关键词： Extended Calogero-Bogoyavlenskii-Schif(eCBS)equation Riccati-Bernoulli equation symmetry analysis integrating factor nonlinear integrable equations