96 euler's equations of motion. 



2. To determine the compoiient changes of the body's moment of 

 momentum. 



At time t the components of the moment of momentum are Aw.^, 

 Bu)^, Coi^ in the directions of the principal axes, where A, B,(J denote 

 the principal moments of inertia. At time t + 8t the components are 



A (lu^ + —r^dt), &c., in iihe directions OA', OB', OC. Employing the 



figu.re in a new sense, the former components may be represented 

 by OA, OB, 00, and the latter by OA', OB', OC. The changes 

 of the moment of momentum in time 8i are therefore AA', BB', 

 GC. Resolving these changes into their components parallel to 

 the axes at time t we get, as in the former case, (observing that 

 FP, PA' are now the displacements in time dt of the point F 



{A(Ui + A —-~dt, o, o), &c.), the following as the resultant changes 



of the moment of momentum in time dt : 



(A — yi - Bw^iog + C (1)^(1)^) dt along OA ; 

 at 



{A(o^w^ + B ~r-^ - Cu)ju}{) dt along OB ; 

 (to 



( - Auj^u)^ + Bw2Ufi + C —J—) 8t along OC . 



The changes per unit time are therefore A — — -{B - C) (o^w^, he, 

 in the directions OA, OB, OG, respectively. 



November 21st, 1878, 



