The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Ni...The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.展开更多
Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of...Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.展开更多
Objective Large igneous provinces （LIPs） are sites of spatially contiguous, rapidly emplaced magmatic rocks, which represent the physical and chemical transfer of material from the mantle to the crust. Exposed with...Objective Large igneous provinces （LIPs） are sites of spatially contiguous, rapidly emplaced magmatic rocks, which represent the physical and chemical transfer of material from the mantle to the crust. Exposed within some continental LIPs are felsic and rnafic plutonic and volcanic rocks. Although their volumes are minor compared to the flood basalts, the plutonic rocks of continental LIPs are often associated with economic deposits of precious metals. Within the Permian Tarim LIP of NW China, there are at least two layered ultramafic-mafic intrusions （e.g. Wajilitag and Piqiang） contain economically important Fe- Ti-V oxide deposits. Spatially associated with these layered ultramafic-mafic intrusions are syenitic and granitic plutons, which have chemical characteristics of A- type granitoids.展开更多
This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under ...This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.展开更多
文摘The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11142014)the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province,China (Grant No. CXLX12_0720)
文摘Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.
基金financially supported by the National Natural Science Foundation of China (Grant No.41703030)research grants from the East China University of Technology (Grants No.DHBK2015323 and RGET1504)the Jiangxi Provincial Department of Education (Grant No.GJJ150556)
文摘Objective Large igneous provinces （LIPs） are sites of spatially contiguous, rapidly emplaced magmatic rocks, which represent the physical and chemical transfer of material from the mantle to the crust. Exposed within some continental LIPs are felsic and rnafic plutonic and volcanic rocks. Although their volumes are minor compared to the flood basalts, the plutonic rocks of continental LIPs are often associated with economic deposits of precious metals. Within the Permian Tarim LIP of NW China, there are at least two layered ultramafic-mafic intrusions （e.g. Wajilitag and Piqiang） contain economically important Fe- Ti-V oxide deposits. Spatially associated with these layered ultramafic-mafic intrusions are syenitic and granitic plutons, which have chemical characteristics of A- type granitoids.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10772025)the Fund for Fundamental Research of Beijing Institute of Technology
文摘This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.
