摘要
旋转坐标系下的圆型限制性三体问题因含非惯性系所附加的影响部分使得动能不是动量的严格二次型,可能导致力梯度辛积分算法的应用遇到困难.从Lie算子运算出发,严格论证了力梯度算子在这种情形下的物理意义仍然像质心惯性坐标系下的圆型限制性三体问题那样是引力的梯度,而不是引力与非惯性力所得合力的梯度,表明了力梯度辛方法适合求解旋转坐标系下的圆型限制性三体问题.通过应用四阶力梯度辛方法、最优化四阶力梯度辛方法和Forest-Ruth辛方法分别求解该问题,进行了数值对比研究,结果显示最优化型力梯度算法能够取得最好精度.还应用最优化型算法计算两邻近轨道的Lyapunov指数和快速Lyapunov指标,确保高精度辛方法能够贯穿于这些混沌指标计算的全过程,以便准确刻画此系统的动力学定性性质.
The kinetic energy of the circular restricted three-body problem in a rotating frame is no longer a standard positive quadratic function of moment, owing to the additional part in the non-inertial rotating frame, which leads to a difficulty in using force gradient symplectic integrators. To address this problem, we show through the calculation of Lie operators that the force gradient operator on the system is still related to the gradient of the gravitational forces from the two main objects rather than that of the resultant force of both the gravitational forces and the non-inertial force exerted by the rotating frame, just as the force gradient operator on the circular restricted three-body problem in an inertial frame. Therefore, it is reasonable to use the gradient symplectic integrators for integrating the circular restricted three-body problem in the rotating frame from a theoretical point of view. Numerical simulations describe that a fourth-order force gradient symplectic method is always greatly superior to the non-gradient Forest-Ruth algorithm in the numerical accuracy, and its optimized version is best. Because of this, the optimized gradient scheme is recommended for calculating chaos indicators, such as Lyapunov exponents of and fast Lyapunov indicators of two nearby trajectories, which is conductive to obtaining a true description of dynamically qualitative properties.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2013年第14期33-40,共8页
Acta Physica Sinica
基金
国家自然科学基金(批准号:11173012
11178002)
南昌大学创新团队项目资助的课题~~
