SOLVABLE (NONRELATIVISTIC, CLASSICAL) N-BODY PROBLEMS ON THE LINE .1.

Several solvable n-body problems on the line are exhibited. They are c haracterized by equations of motion of Newtonian type, m(j)x(j) = F(j) , j = 1,...,n, with the ''forces'' F(j) given as explicit functions of the ''particle coordinates'' X(k) and their velocitieS x(k), k = 1,.. .,n; the forces F(j) generally also depend on some free parameters, so that in each case there is actually a class of solvable models. In th is paper the emphasis is on translation-invariant models, and on value s of n sufficiently small (''few-body problems'') to allow the display of the solution of the initial-value problem in completely explicit f orm.