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摘要: 研究广义Birkhoff系统的Birkhoff对称性问题，并给出此情形下相应的守恒量.将力学系统的等效Lagrange函数的一个定理推广到广义Birkhoff系统，证明了在一定条件下与两组动力学函数B,Rμ,Λμ和B,Rμ,Λμ分别给出的广义Birkhoff方程相关联的矩阵Λ
Abstract: The problem of Birkhoff symmetry for generalized Birkhoffian systems is studied, and the corresponding conserved quantities are given. A theorem known for nonsingular equivalent Lagrangians is generalized to the generalized Birkhoffian systems. We prove that under certain conditions the matrix Λ, which is related with the generalized Birkhoffian equations obtained from two groups of dynamical functions B,Rμ,Λμ and B,Rμ,Λμ, has the property that the traces of all its integer powers are the conserved quantities of the system. An example is given to illustrate the application of the results.
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