DE MOMENTO INERTIAE.

171

fx’W'dM= - A f n cofn cofB + Bfn cof n cofB+D {cofn % -fn % ) cofB-EfyfB + FcofnfB

fx"z"dM ~~A cof n*f$ cof B-B fn* fB cofB + CfB cofB-zDfycofnfBcofB+Ecofn {cofB* ~fB*) + Ffn{cofB*-fB*qui valores fuiU eo magis notandi, quod caiibus, quibus momentui*inertiae fit maximum vel minimum, evanescunt, uti mox videbimus,

PROBLEMA. 27.

438. Inter omnes axes per centrum inertiae dati corporis dudlosdefinire eum, cujus refpcdu momentum inertiae eft vel mrximum velminimum.

SOLUTIO.

Maneant omnia j uti in problemate praecedente, fitque IG axistalis quaefitus, ita ut' determinari oporteat angulos AIF = n et FIG — A.Momentum ergo inertiae refpetfiu hujus axis cum fit f (y"if -f z"z")dM=cAftn* + A cofn *fB 2 + Bcof n * + Bf n * /S 2 4- CcofB*

— zD/tjcoftj cofB* — 2 EcofnfB cofB—2 FfnfB cofB

differentietur duplici modo, sumendo primum n deinde Z- variabile,' etutrumque differentiale nihilo aequale ponatur. Ex priore igitur prodibithaec aequatio

2 Af M cofn co/B* — zBfy cofn cof B* ~zD cofy z cofB * -f zDfn z cofB *+ 2 EfnfBcofB — zFcofnfBcofB = o

quae per — 2 cof B divisa praebet “

- {A- B)ft n cof Yj cofB -j- D{cof n * -fn *)cofB - FfnfB+Feof vJB-ofive fx"f'dM — o : unde colligitur

/Z- r\ -( A~B)fncof n JfD (cofn i -f*i z )

cofB

: tang B —'

Efn-Fcofy

Sumendo autem B variabile pervenimus ad hanc aequationem;

<2 A cofn* fB cofB + 2 Bfn z fBcofB —2 CfB cofB -\-4Dfnc0f yfB cofB- 2 E cofn {cofB*-fB*) - 2 Ffn ( cofB* ~fB z ) = oquae formula efl = _ 2 fx"z"dM. Cum nunc fit2fBcofB=fi2BotcofB z —fB* — cof 2B eritA cofn* f 2 B+ Bfn* fi 2 B—CfzB+2 Dfn cofrjfz B—zEcofycofzB- Ffycof2B=o

Y % unde