By Henry William Watson

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**Additional info for A Treatise on the Application of Generalised Coordinates to the Kinetics o**

**Example text**

Mass of an element ds of the string at P. the vector velo Let p P be the vector from the origin to P, Let fx da be the f>p city of P. Also let pq, pq be the corresponding vectors for a neighbouring 40 EXAMPLES OF point Q of the string. (PP is, PQ) (pp - p Q = 0. ^ =0 Thatis, or, Then, by the condition of inextensibility, constant; that or [24. p ds, Jo being the length of the string. Then, making T a subject to (1), we have by the calculus of variations, s minimum A being an indeterminate multiplier.

WORK DONE BY T5-] 29 IMPULSES. Then employing the notation of the preceding articles we know work done by the impulse must be equal to that the T -Lp+p or , ) j q+tf fp or Let the new velocity q-\-q be denoted by $, then work becomes this ex pression for the =P D Alembert s principle^ Therefore the work done by the impulse whose generalised Also by components are P19 P 2 , . , is 2 If the impulse whose rectangular components are X, Z, at a point of the system whose coordinates are x, y, z and ponent velocities u^ v, w, and if U 9 V^ W be the values of Z act com #, v, w after the impulse, then the work done will be found by substi tuting X, Z, Z for P lt P2 P3 in the above expression and making , each of the remaining components, becomes u+U v+V P4 P5 , , &c w+W zero ; so that it CHAPTEE IT.

Also let pq, pq be the corresponding vectors for a neighbouring 40 EXAMPLES OF point Q of the string. (PP is, PQ) (pp - p Q = 0. ^ =0 Thatis, or, Then, by the condition of inextensibility, constant; that or [24. p ds, Jo being the length of the string. Then, making T a subject to (1), we have by the calculus of variations, s minimum A being an indeterminate multiplier. d\ p + ^Xp" +ds ds ds , 2 p p ds substitute this value of attending to the following 2 cZ known ~ - f jot cZs p+ . p jut in the equation (l), relations, 41 MINIMUM KINETIC ENERGY.

### A Treatise on the Application of Generalised Coordinates to the Kinetics o by Henry William Watson

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