时间尺度上广义Birkhoff系统准对称性与守恒量  

Quasi-symmetry and conserved quantity for generalized Birkhoffian system on time scales

作　　者：宋传静 SONG Chuanjing(School of Mathematics and Physics,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2020年第1期12-17,40,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11802193,11572212);江苏省政府留学奖学金资助项目;江苏省高等学校自然科学基金资助项目(18KJB130005);苏州科技大学科研启动基金资助项目(331812137);苏州科技大学科研基金资助项目。

摘　　要：为揭示时间尺度上力学系统对称性与守恒量内在关系,文章研究时间尺度上广义Birkhoff系统准对称性与守恒量。首先,由时间尺度上的广义Pfaff-Birkhoff原理出发,建立时间尺度上广义Birkhoff系统运动微分方程;其次,研究该系统准对称性的判据,并在时间变化和时间不变两种情形下分别给出其守恒量;最后,举例说明结果的应用。In order to reveal the intrinsic relationship between the symmetry and conserved quantity for mechanical systems on time scales,this paper studies the quasi-symmetry and conserved quantity for generalized Birkhoffian system on time scales.Firstly,the differential equations of motion for generalized Birkhoffian system were obtained from the generalized Pfaff-Birkhoff principle on time scales.Secondly,the criteria for quasi-symmetry for this system were investigated.The conserved quantities were given in two cases of whether the time transforms or not.Finally,the results were illustrated.

关 键 词：准对称性 守恒量 广义BIRKHOFF系统 时间尺度 

分 类 号：O316[理学—一般力学与力学基础]