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离散机电动力系统的对称性和保结构算法
  • 项目名称：离散机电动力系统的对称性和保结构算法
  • 项目类别：面上项目
  • 批准号：10672143
  • 申请代码：A020201
  • 项目来源：国家自然科学基金
  • 研究期限：2007-01-01-2009-12-31
  • 项目负责人：傅景礼
  • 负责人职称：教授
  • 依托单位：浙江理工大学
  • 批准年度：2006
中文摘要：

引入李群方法，提出离散机电动力系统的变分原理，建立了规范格子和非规范格子离散拉格朗日-麦克斯韦差分方程的李对称性、诺特对称性、非诺特对称性和速度依赖对称性理论；得到该系统离散形式的诺特守恒量、非诺特守恒量；建立了超长弹性细杆的对称性理论；给出了线性和非线性机电耦和系统的场积分方法；进行了约束力学系统功能积分关系的研究。引入Lie 群分析方法和数值分析方法，给出离散拉格朗日-麦克斯韦方程的保结构算法；提出了求解非线性薛定格方程、麦克斯韦方程的辛方法；将李群方法、辛算法和保结构数值方法等引入离散机电系统尚属首次，开辟了新的研究领域；得到的对称性理论和保结构算法，可以应用到磁悬浮、交流电机和机器人等机电工程中；丰富和发展了机电动力学的基本理论，展示了对称性理论和数值分析方法广阔的应用前景。

中文主题词： 机电动力系统；对称性；守恒量；数值方法；李群
结论摘要：

英文主题词mechanico-electrical system;symmetry; conserved quantity; Numerical method; Lie group

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 60
  • 3
  • 0
  • 0
  • 1
期刊论文
A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems
Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems
Lie symmetries and conserved quantities for super-long elastic slender rod
Non-existence of conjugate- symplectic multi-step methods of odd order
Symmetry and Hojman conserved quantity of Tzénoff equations for unilateral Holonomic systems
Mei symmetry and new conserved quantity of Tzénoff equations for Holonomic systems
Lie symmetries and conserved quantities of for a two-dimentional nonlinear diffusion equation of con
Damped properties and Noether symmetries of damped free vibration
Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative
Momentum-dependent symmetries and non-Noether conserved quantities for nonconservative Hamilton syst
Non-Noether symmetries and Lutzky conserved quantities for nonholonimic neoconservative dynamical sy
Non-Noether symmetries and Lutzky conserved quantities for mechanico-electrical systems
Hojman conserved quantities of discrete mechanico-electrical systems constructed by continuous symme
The symmetries of the wave equations on new lattices
机电动力系统的动量依赖对称性和非 Noether 守恒量
The symmetries of wave equations on new lattices
Noether symmetries of discrete mechanico-electrical systems
Energy-Work Connection Integration Scheme for Nonholonomic Hamiltonian Systems
A field method for integrating the equations of motion of mechanico-electrical coupling dynamical sy
Noether symmetry and Lie symmetry of discrete holonomic systems with dependent corrdinates
Conserved quantities and conformal mechanico-electrical systems
The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mas
The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems
Structure properties and Noether symmetries for super-long elastic slender rod
A new conserved quantity corresponding to Mei symmetry of Tzénoff equations for nonHolonomic systems
An energy-work relationship integration scheme for nonconservative Hamiltonian systems
An field method for integrating equations of motion of nonlinear Mechanico-electrical coupling dynam
Mei symmetry and new conserved quantity of Tzénoff equations for nonHolonomic systems of Non-Chetaev
Mei symmetry of general discrete holonomic system
Construction of exact invariants of time-dependent linear nonholonomic dynamical systems
HOJMAN CONSERVED QUANTITIES AND LIE SYMMETRIES OF DISCRETE NON-CONSERVATIVE SYSTEMS
Noether symmetries of discrete nonholonomic dynamical systems
Noether conserved quantities and Lie point symmetries of difference Lagrange-Maxwell equations and l
非规范格子离散非保守系统的Noether理论
Explicit symplectic methods for the nonlinear Schrodinger equation
Symplectic discretization for spectral element solution of Maxwell’s equations
离散差分变分 Hamilton 系统的 Lie 对称性与 Noether 守恒量
Euler-Lagrange equation from nonlocal-in-time kinetic energy of nonconservative system
一个带簇个数估计的推广 K-Means 算法
Lie symmetries algebra of one-dimensional nonconservative dynamical systems
Generalized geometry theory on constrained rotating relativistic Birkhoffian systems
离散 Ladrange 系统的 Lie 对称性
矢量波动方程的时空高阶方法
离散差分变分Hamilton系统的Lie对称性与Noether守恒量
离散Lagrange系统的Lie对称性
并行多重网格光滑子JGS与PGS的性能比较
基于融合策略的非下采样Contourlet域SAR图像去噪与仿真分析
非保守动力系统的Lie对称性代数
一个带簇个数估计的推广K-means算法
Conformal invariance and conserved quantities of Appell systems under second-class Mei symmetry
Lie symmetries and conserved quantities for a two-dimentional nonlinear diffusion equation of concentration
Conformal invariance and Hojman conserved quantities for holonomic systems with quasi-coordinates
Noether conserved quantities and Lie point symmetries of difference Lagrange-Maxwell equations and lattices
Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems
A field method for integrating the equations of motion of mechanico-electrical coupling dynamical systems
Structure properties and Noether symmetries for super-long elastic slender rod
完整系统Tzénoff方程的三种对称性及其直接导致的守恒量
会议论文
Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems
Lie symmetry and invariant for a 2D nonlinear Diffusion equations
Energy-work connection integration scheme for mechanico-electrical systems
著作
几类动力学系统的对称性和守恒量研究
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