344 Mr. G. H. Bryan on the Equations of 



Therefore ; 



d ai 



L[ ~dfdp 



-{H + HJ(-tM 



•{g+Mf(--£W 



Application to the Equations of Motion. 



7. The equations of motion of the solid may now be written 

 down at once. Let X' be the kinetic energy of the solid, T 

 the total kinetic energy = X + X' ; and suppose that the motion 

 takes place under the action of a system of external impressed 

 forces and couples designated by X, Y, Z, L, M, N. Then 

 the effective forces and couples to which the motion of the 

 solid itself is due are X — Xj . . ., L — Lj . . ., respectively, and 

 the six equations of motion of the solid referred to the moving- 

 axes are of the form 



d-bz 1 ax' ai' ax' ar T T , ia . 



at Op ov Ow oq 1 ^r v ; 



Hence, on substitution, we see that the required equations 

 of motion are found by writing T for X and X, Y, Z, L, M, N 

 for X 1? Yj, Z l5 L l3 Mi/Nx in equations (9) (11). The resulting 

 equations may be written : 



x= ^^-4^ + v + % + 9 ( 14 > 



tfBT /BT \ /BT A 



where f, ??, £, X, /*, v are defined by the equations 



