Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformati...Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.展开更多
This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The ...This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The differential equations of motion of the system are established, and the definition of Lie symmetry for the system is given. The conditions under which a Lie symmetry can directly lead up to a generalized Lutzky conserved quantity and the form of the new conserved quantity are obtained, and an example is given to illustrate the application of the results.展开更多
We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation v...We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.展开更多
This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the ...This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system＇s results.展开更多
This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exist...This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.展开更多
为探讨分布式能源站(distributed energy station,DES),这一能源系统中的重要能源转换环节,研究其站内规划与多站之间的多能互补特性,并兼顾考虑能量的“数量”与“品质”双重价值属性,将量质协同约束纳入DES规划范畴,为此,该文提出一...为探讨分布式能源站(distributed energy station,DES),这一能源系统中的重要能源转换环节,研究其站内规划与多站之间的多能互补特性,并兼顾考虑能量的“数量”与“品质”双重价值属性,将量质协同约束纳入DES规划范畴,为此,该文提出一种多区域电-冷-热互联DES量质协同规划方法。首先,建立DES互联冷管道传输模型;其次,采用能源集线器建立考虑电-冷-热互联协同、新能源接入的DES综合模型;在此之后,基于混合整数线性规划,以互联系统总成本最低为优化目标,引入㶲效率约束,构建多区域电-冷-热互联DES量质协同规划模型;最后,通过算例验证了规划模型的合理性与可行性。展开更多
文摘Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272021 and the Natural Science Foundation of High Education Department of Jiangsu Province under Grant No. 04KJA130135
文摘This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The differential equations of motion of the system are established, and the definition of Lie symmetry for the system is given. The conditions under which a Lie symmetry can directly lead up to a generalized Lutzky conserved quantity and the form of the new conserved quantity are obtained, and an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos.10672143 and 60575055)
文摘We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.
文摘This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system＇s results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)the Fund for Fundamental Research of Beijing Institute of Technology (Grant No 20070742005)
文摘This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.
文摘为探讨分布式能源站(distributed energy station,DES),这一能源系统中的重要能源转换环节,研究其站内规划与多站之间的多能互补特性,并兼顾考虑能量的“数量”与“品质”双重价值属性,将量质协同约束纳入DES规划范畴,为此,该文提出一种多区域电-冷-热互联DES量质协同规划方法。首先,建立DES互联冷管道传输模型;其次,采用能源集线器建立考虑电-冷-热互联协同、新能源接入的DES综合模型;在此之后,基于混合整数线性规划,以互联系统总成本最低为优化目标,引入㶲效率约束,构建多区域电-冷-热互联DES量质协同规划模型;最后,通过算例验证了规划模型的合理性与可行性。
