VllOBLKMS.

123

Q sin 9 - R — = 0.(2),

ds •

two equations and five unknown quantities R, 9, x, y, s : sinceequations (1) (2) are the only conditions of equilibrium, theother three equations must be among the quantities 9, x, y, s :they are

.P), £->/,7g. w,

x dx dx 2

and <p (■»> y) = o .(5)

the equation to the curve. These five equations will solvethe problem when we select any particular curve.

The elimination of R from (l) and (2) gives

W — Q (cos 9 + ~ sin 0) = 0,dx

or W - Q (- + - \ = 0 by (3) : r 2 = X s + y 2 ,

\T V CLOD}

or Wdx — Qdr - 0

the equation of virtual velocities which we should have ob-tained from Art. 24.

Suppose the curve is a circle the centre being at a verticaldistance c from the point B : then a being the radius

y~ + (x — c) 2 = a 2 ;

dr c

r 1 = or + y 2 = a? - c + 2cx; — = -;

dx r

Q

w’

w 2 ’

.•. x =

r 2 - a s + c 2 (Q 3 + W 3 ) c 2 - W 2 a s

2 c

and the position of W is known.

2 c W 3