Evolution of Stable Solution to Chaotic Solution in Three-Body Motion
The enhanced SPRK(Symplicit Partitioned Runge-Katta)method is used in this paper to numerically calculate the three-body motion process,and the motion law and stability under varied initial conditions are investigated.The improved method enhances the accuracy of calculation while maintaining the speed of the algorithm.The solution to the three-body issue is discovered to have an obvious nonlinear chaotic effect,and the motion can be converted from a stable periodic solution to a chaotic solution by applying some minor modifications in the initial parameters of the known stable periodic solution.Further analyzing the stability of Lagrange points,it is discovered that perturbations can cause motion from a stable periodic solution to an unstable chaotic solution at unstable Lagrange points.The stability of the orbits in different regions is verified for objects restricted within the Hill sphere,and the motion orbits are significantly disordered,especially for objects close to the sphere.These findings are helpful to improve our understanding of the three-body problem in physics and mathematics.
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