Separation of variables for ordinary differential equations

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In case of the PDE's the concept of solving by separation of variableshas a well defined meaning. One seeks a solution in a form of aproduct or sum and tries to build the general solution out of theseparticular solutions. There are also known systems of second orderODE's describing potential motions and certain rigid bodies that areconsidered to be separable. However, in those cases, the concept ofseparation of variables is more elusive; no general definition isgiven.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. ...