能量稳定化方法在平面圆形限制性三体问题中的应用

能量稳定化方法在经典力学中应用广泛,具有重要的研究价值.基于平面圆形限制性三体问题存在唯一的雅克比积分形式,可采用能量稳定化方法保持该孤立积分.实验表明:加入稳定化后的数值算法能保持雅克比积分常数的稳定性,同时提高了相应坐标量和速度量的数值结果精度.通过非线性动力学研究方法如庞加莱截面和功率谱分析进一步表明能量稳定化方法能够有效的避免数值误差产生的混沌行为,从而准确地揭示了相空间结构.

Application of Energy Stabilization Method in the Planar Circle Restricted Three-body Problem

Energy stabilization method is widely used in classical mechanics,and it is well worth researching.Based on the planar circle restricted three-body problem,there exists only Jacobi integral form.We can take the energy stabilization method to keep it isolating integral.The experiment shows that the stabilization method can make Jacobi integral value stable and improve the precision of corresponding coordinate amount and speed amount.Through the nonlinear dynamics research methods such as the analysis of Poincare section and power spectrum,further study has shown that energy stabilization method can effectively avoid the chaotic behavior caused by numerical errors.Therefore,it reveals exactly what the phase space structure is.