;zr CAPUT XVII. PLENIOR EXPLICATIO

feu

n

M

O +

ff(qq + rr )

’)=

I +

faax (qy -f ra) fp. (yy + zz)

hincquc

n

CC y 2 gCC 2 g

2gcc -f /an (M + rz) — fccp (yy + as)

M

2gcc + 2 gff(qq + rr)

C O R O L L. 3.

g6o, Ex aequationibus IV. V. VI. colligitur, ut jam ante notavimus»xdp + ydq -f zdr = 0, quae aequatio, cum iit pp -f- qq 4. rr = 1 „ locoaequatjonum V„ et VI, ulurpari potefi. At aequationum VII, VIII. IXunicam traifiafie fufficiet, quod negotium pofiremo loco erit jfufcipiendum.

C O R O L L. 4.

H61. Inventis autem quantitatibus x, y et z, ob cof«* 4- cofC*+ cofy* — 1 erit celeritas angularis n—\f (xa: + yy -f- zs) hincque vi-ciffiin arcus «, S, y concluduntur; nempe

x

coi a — -; cof£ — et cofy =

H 8 L

PROBLEMA 99 .

2, Aequationes differentiales ante inventas, quibus motus turbinisexprimitur, ad integrationem perducere, quantum fieri licet.

SOLUTIO.

Primo fiatim patet efTc x — confi: ponamus ergo x = A, et reli-quae aequationes integrandae erunt

. A (aa — cc) zdt lYlfgrdt

'°- ^ + —-— = -

cc Mcr

z

Jz —

A (aa — cc) ydt — zTlfgqdt

cc

3 0 . dp — dt (qz — ry )4 0 . ydq + zdr = — Adp

II fddp

— I +

Mrr

et pp + qq + rr — r.

exifiente w — .

M 2 gdt 1

J^nnc i °, q + 2 0 , r fupeditat hanc aequationem

A (aa — cc)

qdy + rdz + --—-- dt (qz — ry) = o

quae ob dt (qz — ry) dp abit in hanc;

qdy