时间尺度上Birkhoff系统的积分因子和守恒量

Integrating factors and conserved quantities for Birkhoffian systems on time scales

研究时间尺度上Birkhoff系统的守恒量,建立时间尺度上Birkhoff系统的积分因子与能量方程,构建利用积分因子法求解该系统守恒量的守恒定理.时间尺度上Hamilton系统与时间尺度上Lagrange系统的能量方程、积分因子和守恒定理是其特例,最后举例说明结果的应用.

This paper studied the conserved quantities of Birkhoffian systems on time scales. The method of integrating factors was proposed to find the conserved quantities of Birkhoffian systems on time scales. And the energy equation of Birkhoff’s equations was established on time scales. The integrating factors and conservation theorems for Birkhoffian systems on time scales were investigated. The integrating factors and conservation theorems for Hamiltonian systems and Lagrangian systems on time scales were special cases of Birkhoffian systems on time scales. Finally, an example was given to illustrate the application of the results.