Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..
Now if yi and y 2 are the displacements due to the two trains separately, and y=yl+y2, the two separate forces are Tdy/dx and Tdy 2 /dx, while that due to y is Tdy/dx.
A long story book, called the Djiung yi (Sgrungs gyi gsungs ?), and regarded as the national epic in Kham, has been partly seen by Desgodins and Baber.
The force at A1 may be replaced by its components Xi, Yi, parallei to the co ordinate axes; that at A1 by V1 its components X2, Yf, and so on.
Yi at Ai may be replaced by a force Yi at 0 together with a couple x1 Y1.