 The method of generalised co-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis.Instead of following the motion of each individual part of a material system, as D'Alembert and Euler had done, he showed that, if we determine its configuration by a sufficient number of variables "x", called generalized coordinates, whose number is the same as that of the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms of those variables, and the differential equations of motion thence deduced by simple differentiation.For example, in dynamics of a rigid system he replaces the consideration of the particular problem by the general equation, which is now usually written in the form

where "T" represents the kinetic energy and "V" represents the potential energy of the system.