Moderk Methods of Treating Dynamical Problems and in Particular the Problem of Three Bodies

the solution of a certain partial differential equation of the second order which is reduced by quadratures to a linear partial differential equation of the first order. The more complicated types of problems in the calculus of variations are examined in a similar manner. But in no type except the simplest are the differential equations which present themselves as necessary conditions of general character, i. e., the system of extremals is no longer an arbitrary system of curves or surfaces (in space of any number of dimensions). Thus an integral of type