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A solution method for decomposing vector fields in Hamilton energy
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作者 Xin Zhao Ming Yi +2 位作者 Zhou-Chao Wei Yuan Zhu Lu-Lu Lu 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期645-653,共9页
Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the... Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems. 展开更多
关键词 Hamilton energy dynamical systems vector field exterior differentiation
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Interior and Exterior Differential Systems for Lie Algebroids
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作者 Constantin M.Arcus 《Advances in Pure Mathematics》 2011年第5期245-249,共5页
A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Frobenius type is... A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Frobenius type is obtained. Extending the classical notion of exterior diffential system (EDS) to Lie algebroids, a theorem of Cartan type is obtained. 展开更多
关键词 Vector Bundle Lie Algebroid Interior Differential System exterior Differential Calculus exterior Differential System
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ON DEGENERATE WEAKLY (K_1,K_2)-QUASIREGULAR MAPPINGS 被引量:1
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作者 高红亚 李彤 《Acta Mathematica Scientia》 SCIE CSCD 2008年第1期163-170,共8页
The authors first give the definition of degenerate weakly (K1,K2)-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a usef... The authors first give the definition of degenerate weakly (K1,K2)-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity. 展开更多
关键词 Degenerate weakly (K1 K2)-quasiregular mapping exterior power exterior differential form McShane extension
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INVARIANT FORM AND INTEGRAL INVARIANTS ON KAHLER MANIFOLD
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作者 张荣业 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第2期269-278,共10页
The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics... The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential 展开更多
关键词 Kahler manifold symplectic manifold invariant form integral invariant vector field form field Lie derivative exterior differential
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DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACETIME (Ⅰ)
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作者 Zhang Rongye (Institute of Mathematics, Academia Sinica, Beijing 100080, P R China) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第7期825-835,共11页
By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is est... By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued. 展开更多
关键词 Riemannian manifold connection absolute differential Lie derivative exterior differential co_moving time derivative fiber bundle duality pairing
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LAGRANGIAN VECTOR FIELD ON KOHLER MANIFOLD
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作者 张荣业 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第9期901-908,共8页
In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
关键词 Kahler manifold tangent and cotangent bundle fiber Connection tensor product exterior product exterior Differential absolute differential symplectic form Lagrangian Form Hamiltonian vector field Lagrangian vector field dynamical group INFINITESIMAL
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