In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two ca...In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.展开更多
地震沉积学在高频率层序和沉积体系研究中有着特殊的优势。90°相位地震资料的振幅可以和岩性测井曲线对应,对地震资料进行90°相位转换后可以通过地震振幅分析岩相。地层切片技术可以在平面上显示相对同一地质沉积时间的沉积...地震沉积学在高频率层序和沉积体系研究中有着特殊的优势。90°相位地震资料的振幅可以和岩性测井曲线对应,对地震资料进行90°相位转换后可以通过地震振幅分析岩相。地层切片技术可以在平面上显示相对同一地质沉积时间的沉积分布特征,再结合岩性测井资料可以较准确分析沉积体系。美国南得克萨斯地区Webb县Gold River North油田上白垩统Olmos组钻井资料较少,采用地震沉积学方法对其分析,可以识别出一套完整的三角洲体系,其中包括前三角洲亚相、三角洲前缘亚相、三角洲平原亚相、曲流河相和下切谷沉积等,其中河道砂、河口砂坝和下切谷沉积物是有利的储层。展开更多
基金supported by the National Natural Science Foundations of China (Grant Nos.11072218 and 11272287)the Natural Science Foundations of Zhejiang Province of China (Grant No.Y6110314)
文摘In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.
文摘地震沉积学在高频率层序和沉积体系研究中有着特殊的优势。90°相位地震资料的振幅可以和岩性测井曲线对应,对地震资料进行90°相位转换后可以通过地震振幅分析岩相。地层切片技术可以在平面上显示相对同一地质沉积时间的沉积分布特征,再结合岩性测井资料可以较准确分析沉积体系。美国南得克萨斯地区Webb县Gold River North油田上白垩统Olmos组钻井资料较少,采用地震沉积学方法对其分析,可以识别出一套完整的三角洲体系,其中包括前三角洲亚相、三角洲前缘亚相、三角洲平原亚相、曲流河相和下切谷沉积等,其中河道砂、河口砂坝和下切谷沉积物是有利的储层。
