Abstract: The present article gives a historical survery of G.D. Birkhoffs seventh problem which is an inquiry about the topological structure of the set of definition of the reduced differential equations of motion. Recent advances in the problem and their meaning have been briefly indicated.The classical 3-body problem concerns how the three particles should move under their mutual Newtonian attraction. By a particle we mean a goometrical point endorsed with a constant positive number m which is called mass.

Key words: extended linear complementarity problem, modified SLP algorithm, global convergence