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contact Extension and Symplectification

应用数学学报:英文版 2023年第4期39卷 962-971页

作者： Qi-huai LIU An XIE Chao WANG School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilin 514001China School of Mathematical Sciences Yancheng Teachers UniversityYancheng 224002China Center for Applied Mathematics of Guangxi(GUET) Guilin 514001China

This paper mainly studies the contact extension of conservative or dissipative systems, including some old and new results for wholeness. Then extension of contact system is corresponding to the symplectification of contact Hamiltonian system. This is a reciprocal process and the relation between symplectic system and contact system has been discussed. We have an interesting discovery that by adding a pure variable p,the slope of the tangent of the orbit, every differential system can be regarded as an independent subsystem of contact Hamiltonian system defined on the projection space of contact phase space.

关键词： contact extension contact Hamiltonian system contact transformation

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ON THE ADJOINT SYMPLECTIC SUBSPACE ITERATION METHOD FOR THE DOMINANT EIGEN-SOLUTIONS OF THE HAMILTONIAN MATRIX

引用

Progress in Natural Science:Materials International 1992年第4期 332-342页

作者：钟万勰 College of Swansea Dalian 116023 Department of Civil Engineering PRC Research Institute of Engineering Mechanics Dalian University of Technology University of Wales Visiting Professor

In the case of the very large dimensions of the linear control system,the method to find its solutionis still of much concern today even for the time-invariant *** on the simulation of the structuralmechanics with the optimal control theory,the (?)djoint subspace iteration method is proposed in thepresent *** is quite different from the usual approximate method for large systems,which used toreduce the state space of the original system and then to find the solutions of the reduced *** method,however,keeps the original system unchanged,and rotates the adjoint symplectic subspacesin the whole state space with the iterations,which is the combination of the state space and the *** the whole state space is *** the iteration converges,the dominant eigen-solutions of the original system are *** symplectic transformation reflects the characteristicsof the Hamiltonian *** is a kind of contact transformation,and thus its reduced subspace from thetransformed whole state space will be able to keep the dominant characteristics of the original *** other hand,the usual reduced state space method corresponds to the point transformation in themathematical theory of the Harailtonian *** dominant characteristics of the original system willunavoidably be disturbed in the reduced state *** the adjoint symplectic subspace iteration meth-od has a great superiority.

关键词： LQ control Hamiltonian matrix contact transformation symplectic matrix adjoint symplectic subspace iteration method

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