## Qr Sentence Examples

- 2
**qr**., 20 cwt. - If then we put a negative point-charge -
**qr**/d at B, it follows that the spherical surface will be a zero potential surface, for q rq 1 (24). - If a force Q acting at R maintains equilibrium,
**QR**/4 = (P - p)r =T. **Qr**,, be the generalized coordinates of any dynamical system, and let pi, P2,- If the system is supposed to obey the conservation of energy and to move solely under its own internal forces, the changes in the co-ordinates and momenta can be found from the Hamiltonian equations aE aE
**qr**= 49 - 1 57., gr where q r denotes dg r ldt, &c., and E is the total energy expressed as a function of pi, qi,. - In the time dt which the wave takes to travel over MN the particle displacement at N changes by
**QR**, and**QR**= - udt, so that**QR**/MN = - u/U. - But
**QR**/MN = dy/dx. - Then the reflected ray
**QR**and the ray reflected at R, and so on, will all touch the circle drawn with ON as radius. - Then
**qr**/ro = hk/hg or ro =W (l-x-a)/l, which is the reaction at A and shear at any point of AD, for the new position of the load. - Comparing this equation with ux 2 +vy 2 +w2 2 +22G'y2+2v'zx+2W'xy=0, we obtain as the condition for the general equation of the second degree to represent a circle :- (v+w-2u')Ia 2 = (w +u -2v')/b2 = (u+v-2w')lc2 In tangential q, r) co-ordinates the inscribed circle has for its equation(s - a)
**qr**+ (s - b)rp+ (s - c) pq = o, s being equal to 1(a +b +c); an alternative form is**qr**cot zA+rp cot ZB +pq cot2C =o; Tangential the centre is ap+bq+cr = o, or sinA +q sin B+rsinC =o. - +(s - b)pq= oor -
**qr**cot 2A+rptan ZB +pgtan 2C=o,with centre - ap+bq+cr = o. - If we now apply them to the case of a rigid body moving about a fixed point 0, and make Ox, Oy, Oz coincide with the principal axes of inertia at 0, we have X, u, v=Ap, Bq, Cr, whence A (B C)
**qr**= L, - + (c,~, oa,,,)q,, =
**Qr**, (28) - Equality of the angles of incidence and reflection, that the reflected ray
**QR**is such that the angles RQC and CQP are equal; to determine the caustic, it is necessary to determine the envelope of this line. - Since an, = a,r, the coefficient of Q, in the expression for
**qr**is identical with that of Q,- in the expression for q,. - If we omit the gyrostatic terms, and write
**qr**= Cre, we finc~, for a free vibration, (aj,1~2 + birX + Cm) C~ + (asrX2 + birX + Cm) C2 + - These variables represent the whole assemblage of generalized co-ordinates
**qr**; they are continuous functions of the independent variables x, y, 1 whose range of variation corresponds to that of the index r, and of 1.