The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in thispaper.The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry.Thecrite...The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in thispaper.The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry.Thecriterion when a conserved quantity may be obtained from Mei symmetry is also deduced.An example is discussed forapplications of the results.展开更多
对于带约束的力学系统的最优控制,约束系统离散力学最优控制(Discrete Mechanics and Optimal Control for Constrained Systems,DMOCC)采用了"先离散,后变分"的方法,结合离散零空间法,能很好地保持系统的物理特性,其模型方...对于带约束的力学系统的最优控制,约束系统离散力学最优控制(Discrete Mechanics and Optimal Control for Constrained Systems,DMOCC)采用了"先离散,后变分"的方法,结合离散零空间法,能很好地保持系统的物理特性,其模型方程可表示为非线性等式约束的优化问题,通常采用标准序列二次规划(Sequence Quadratic Program,SQP)算法求解。由于约束条件的规模大,SQP算法的计算效率不高。相对于SQP,内点法具有收敛性好、稳定性强的特点。在对DMOCC约束条件的特点进行分析之后,将内点法用于DMOCC的数学模型进行数值计算,能有效提高计算效率。曲柄滑块的数值仿真证明了在数值精度一致的情况下,内点法具有效率上的优势。展开更多
After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection ...After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection betweengroupoids variation and the methods of the first and second discrete variational principles.展开更多
基金National Natural Science Foundation of China under Grant No.10672143
文摘The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in thispaper.The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry.Thecriterion when a conserved quantity may be obtained from Mei symmetry is also deduced.An example is discussed forapplications of the results.
文摘对于带约束的力学系统的最优控制,约束系统离散力学最优控制(Discrete Mechanics and Optimal Control for Constrained Systems,DMOCC)采用了"先离散,后变分"的方法,结合离散零空间法,能很好地保持系统的物理特性,其模型方程可表示为非线性等式约束的优化问题,通常采用标准序列二次规划(Sequence Quadratic Program,SQP)算法求解。由于约束条件的规模大,SQP算法的计算效率不高。相对于SQP,内点法具有收敛性好、稳定性强的特点。在对DMOCC约束条件的特点进行分析之后,将内点法用于DMOCC的数学模型进行数值计算,能有效提高计算效率。曲柄滑块的数值仿真证明了在数值精度一致的情况下,内点法具有效率上的优势。
基金National Key Basic Research Project of China under Grant No.2004CB318000National Natural Science Foundation of China under Grant Nos.10375038 and 90403018
文摘After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection betweengroupoids variation and the methods of the first and second discrete variational principles.
