Karl Sundman found a power series solution of this system that is a function of the cube root of time and converges for nonzero initial angular momentum.
This systemâs topologies belong to conjugacy classes of the free group on two letters. This systemâs âgogglesâ and âyarnâ topologies have reflection symmetries about two orthogonal axes of the shape-space sphere. This system has 16 known types of solutions, including the Broucke-HÃ©non and figure-eight families. Karl Sundman found a power series solution of this system that is a function of the cube root of time and converges for nonzero initial angular momentum. A special case of this system has a single constant of motion that equals negative two times total energy per unit mass in the synodic frame of reference. That restricted version of this system has five constant-pattern solutions known as Lagrange points. This system has no general solution that can be written in terms of algebraic expressions and integrals, as proven by Henri PoincarÃ©. For 10 points, name this system exemplified by the motion of the earth, moon, and sun due to their mutual gravitational influence.
This systemâs topologies belong to conjugacy classes of the free group on two letters.
classical three-body problem or system