By Octav Onicescu (auth.)
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Additional resources for Invariantive Mechanics
Following the principle of the invariantive mechanics we must ftrst make precise the Euclidean invariants of the dynamic state of the system. M1 + 82 ([)~- l)x1 ). e.
4th. 49 §3. Inertial Mechanics of a Two Body System 1. Euclidean Invariants of the System. We shall consider first the case n = 2, which is sufficiently complex and rich in new mechanical aspects. A simpler notation has been adopted for the invariants, since we have only one distance vector We put (1) Then We have, in that case, hence (2) for any~. In the above expression we have (3) where we have written Ha instead of dH/da etc. and we must consider Then the second member of (3) becomes 50 eSt, llx 1 , The equations of motion.
H (x, t) + 112 (19) h E rhrk ahk (x, t) + h,k + 1 12 I:rhrk [ahk(xl +ulrl,x2+u2r2,x2+u3r3,t)-ahk(x,t)], h,k 43 where lu 1 1, lu 2 1, lu 3 I < 1. la (x,t) + where 'J ~ € = E ftj tk j,k 1c E it) (20) Jl,jaj (x,t) + 1/2 EJI,jk ajk (x,t) + €, j,k 'J• ~ dp ' it/. dp ca:jk (x 1 + u 1 t 1 ,x 2 + u2t2 ,x3 + u3t3. L and a. j,k= 1,2,3 J a bejng the vector (al' a2' a3' ao ). I (h = 1, 2, 3), H consisting of a number of terms of the form of an order lower than KA. 3 and which are assumed to be negligible. j and tjk are invariant characteristics of the body C and a together with its derivatives ai' ajk are continuous functions depending only on x and t.
Invariantive Mechanics by Octav Onicescu (auth.)