Download A Course of Mathematics for Engineers and Scientists. by Brian H. Chirgwin, Charles Plumpton PDF

Download A Course of Mathematics for Engineers and Scientists. by Brian H. Chirgwin, Charles Plumpton PDF

By Brian H. Chirgwin, Charles Plumpton

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Additional resources for A Course of Mathematics for Engineers and Scientists. Theoretical Mechanics

Example text

Zero virtual work, is 3 Wa cos0 00 + Wa cos

T = wm. Note that the tension in this special case has been calculated after writing down the equation of virtual work for the system under consideration in the general case. We do not insert the values of 0 and φ corresponding to the specified configuration until the equation of virtual work (3) and the first order variation (1) of the equation of constraint have been written down.

All t h e rods are pin-jointed a t A, B, C and D and a weight w is a t t a c h e d to C. A virtual displacement is made in t h e system such t h a t t h e length of AB is increased, the others remaining constant in length. If 2δθ is t h e increase in t h e angle ACB and δφ is the increase in BAD, prove t h a t δθ -f- δφ = 0 . Hence prove t h a t the tension in AB is (7 W -f 4w)/2 } 3 . CHAPTER I I I CONTINUOUSLY DISTRIBUTED FORCES 3:1 A uniform, flexible, inelastic string hanging under gravity In this and a perfectly Chap.

The Principle is capable of greater generalisation t h a n the methods of resolution and is used extensively in more advanced mechanics t o discuss very general systems and obtain results of a wide applicability. I t must, however, be emphasised t h a t we have proved the Principle only for the equilibrium of a particle a n d of a rigid body, or for systems formed from such bodies hinged together or rigidly connected. We assume its t r u t h for a much broader class of mechanical systems including flexible A a n d elastic bodies, continuously distribu t e d forces, gravitation, action a t a distance, etc.

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