两自由度微扰力学系统的二阶近似守恒量

SECOND ORDER APPROXIMATE CONSERVED QUANTITIES OF TWO DIMENSIONAL PERTURBED MECHANICS SYSTEM

把微扰力学系统视为未受微扰系统与微扰项的迭加,并选择合适的方法求得未受微扰系统的精确守恒量I0.从近似守恒量的性质出发,建立守恒量的一阶微扰项系数I1与精确守恒量I0、守恒量的二阶微扰项系数I2与守恒量的一阶微扰项系数I1及精确守恒量I0的递推关系.考虑微扰项对精确守恒量以及对守恒量的一阶微扰项系数的影响,利用递推关系并直接积分求得二阶近似守恒量.文中用此方法研究了一微扰力学系统的二阶近似守恒量,并得到2个稳定的二阶近似守恒量.

t We consider the perturbed mechanics system as the combination of unperturbed system and perturbed terms, we can select a suitable method to obtain the exact conserved quantities I0 of unperturbed system. Based on the characteristic of the approximate conserved quantities, the recursion relations between the first order per- turbed coefficient 11 of conserved quantities to the exact conserved quantities I0 and the second order perturbed co- efficient 12 to the first order perturbed coefficient 11 of conserved quantities and the exact conserved quantities I0 are established. We calculate the influence of perturbed terms on exact conserved quantities and on the first order perturbed coefficient, according to the recursion relation between the second order perturbed coefficient to the first order perturbed coefficient of conserved quantities and the exact conserved quantities, we obtain the second order approximate conserved quantities of the system by direct integral method. An actual perturbed mechanics system is studied in this paper, and two stable second order approximate conserved quantities are obtained by u- sing this method.