If r be the number of quotients in the recurring cycle, we can by writing down the relations connectin g the successive p's and q's obtain a linear relation connecting p nr +m, t'(n-1)r +m, +m in which the coefficients are all constants.
The conditions (~) then lead to IA(AC) 2, ,2 (AC)(BC) 1 ~ tO qs B(BC)~ AB r0, C(BC) r~
It is implied in the above description of the system that the Cartesian co-ordinates x, y, z of any particle of the system are known functions of the qs, varying in form (of course) from particle to particle.
The coefficients arr, a,~, are called the coefficients of inertia; they are not in general constants, being functions of the qs and so variable with the configuration.
This solution, taken by itself, represents a motion in which each particle of the system (since its displacements parallel to Cartesian co-ordinate axes are linear functions of the qs) executes a simple vibration of period 21r/u.