Separation of variables for ordinary differential equations

Abstract: In case of the PDE's the concept of solving by separation of variables has a well defined meaning. One seeks a solution in a form of a product or sum and tries to build the general solution out of these particular solutions. There are also known systems of second order ODE's describing potential motions and certain rigid bodies that are considered to be separable. However, in those cases, the concept of separation of variables is more elusive; no general definition is given. In this thesis we study how these systems of equations separate and find that their separation usually can be reduced to sequential separation of single first order ODE´s. However, it appears that other mechanisms of separability are possible.