A theorem on linear subproblem of newtonian N bodies

Abstract

Linear subproblem is a subclass of the Newtonian N-body problem where configuration space is a linear subset of R^<vN> (v = 2 for planar problern, v = 3 for spatial problem). If its degree of freedom (i.e., dimension of configuration space) is f(< vN), then it is called a linear f-subproblem. In this paper, we show a theorem on linear subproblems, i.e., the general planar three-body problem cannot be a linear 3-subproblem.