By Ken Butti

ISBN-10: 0917352084

ISBN-13: 9780917352089

Sm 4to, 1980, PP.289,

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Integration leads to vet) set) = = J a,(1) dt = Jf, (t) dt = f,(t) + C, J vet) dt = J [f,(t) and x dt = /,(t) + C,t + b Figure 4. Motion in a plane: a general, b circle. = 1I(t) + (v 2/R)e n = v(t)e, (v(t); v2/R) t and x across the arc length sex) C2· The constants are determined from the initial conditions vet = t,) = v, and set = t,) = s, or equivalent conditions. From v(t) = a,(t) it follows that, in cases in which vet) assumes an extreme value (where v = 0), in the a" t-diagram the function a,(t) passes through zero.

Q(s) = q(x) dx/ds = q(x) cos", = (19) to Fig. 34a, q(x)/ ~I = q(x)/FH· ditionsy(x = Xl) = y, andy(x the given cable length L + y" and therefore, according to Eq. (19), y" Figure 34. Cable; a dement, b cable under its own weight, cable under point load. (20) The solutions to these differential equations produce the catenary curve y(x). The two integration constants that occur in the process and the unknown (constant) horizontal tensile force FH follow from the boundary con- = C = x 2 ) = y" as well as from J = J~I + ds y'2 dx.

42e). With the results for the fIXed and free pulley, FI = 1)F, F,=1)' FI = 1)2 F, etc. Equilibrium for the freed lower hlock leads to l 2. F( 1) If a cylindrical body or a body of similar shape rolls on a supporting surface (Fig. 42a), the deformation of the supporting surface and of the body produces a resultant lhat is directed at an oblique angle, the horizontal compotllent of which is the resisting force FW' If the motion is uniform, the driving force E, must retain the body in equilibrium.

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A Golden Thread: 2500 Years of Solar Architecture and Technology by Ken Butti


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