( 746 ) 
| 
Zn, gr zj ET, (M1 VER qa) 
r=l 
ig 
tol 
where H, represents a homogeneous function of order three, and 
Pg = O73, “+ Draga + Grsq5- 
The equation of LAGRANGE for the coordinate q, runs: 
see PRES SS Ee A eee UL Me ep 
947,79 = ze inde a= ( do Fey Ja)Grt 3 ee + 4439093 > Og i 
r= r= == G1 
When in the terms of the second member qe is replaced by —7,7q,, 
then in the case of the supposed relation we have to regard as 
disturbing in this equation the terms with os and those with q,q,. 
Omitting all the remaining terms of a higher order the equation 
becomes : 
gq, + Nee EN tgs IRE eo PaO yt ees Cagle Ons at ED 
(p being the coefficient of the term q,g,7, in //,). 
We may now replace q,g, by #,7,4,q;, because these two products 
furnish the same disturbing term when we substitute for g, and q, the 
expressions to be taken at first approximation. We then find: 
ntm a= Edag a Ns + bijltje Melt de De er ee 
Putting in the second member 7, + n, —n, = 0 we finally find: 
drieen Gj == Mgt Ora Wa Menn bral or PAGE 
In this way we can also simplify the two other equations; we 
must then bear in mind that in the second equation 14: must be 
replaced by 7,7,4,7;, in the third equation however q,g, by —n,n,q,qs- 
The result is that the equations of motion are to be written as 
follows : 
dee nr Gp = a lr Be te ed EN 
where 
me en Di, My Ms — Ea, Ns) } V1 Ja Jar 
If, however, we take as abridged 3*¢ equation 
gs + (, dn) gs = 9; 
then we find: 
— Sn — / , app elo Ì 
kip (ass 2, no + Oja % Ms Che Nij 3) 5 91 Ja Ia 7— 
— o(n, Arn) Gs =P Aula Ga 0 (we Ms) Gi 
Den 2 ij — 
Pure relation n, +n, —n, = 0. 
-§ 7. As first approximation of system (1) we take: 
