Vector Analysis And Quaternions

Cover Vector Analysis And Quaternions
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k 2m 2m 2m ' 2 (in a) 2(mb) 2mc therefore x=—^ — , y = — ^ — , z= — — 2m 2m 2m Example. — Given 5 pounds at 10 feet 45°//30° and 8 pounds at 7 feet 6o°//45° ! find the moment when both masses are transferred to 12 feet 75°//6o°.
m 1 A 1 = 5o(cos 30°?' -f- sin 30 cos 45°/+ sm 3°° sin 45°^)» m 2 A^ = 56(cos 45°?-f- sin 45 cos 6o°j-\- sin 45 sin 60° k), (m 1 -f- m^)R = i56(cos 6o°z -f- sin 6o° cos 75^' -f- sin 6o° sin 75°/£), moment = m l A 1 -j- m 2 A^ — (m 1 -j- w 2 )-^.
Composition of a Located
... Vector Quantity. — Let F A de- note a force applied at the extremity of the radius-vector A.
As a force F — F may introduced at the ex- tremity of any radius-vector R, we have F A -(F-F) R + F A = F R + V(A - R)F This equation asserts that a force F applied at the extremity of A is equivalent to an equal force applied at the extremity of R together with a couple whose magnitude COMPOSITION OF QUANTITIES. 37 and direction are given by the vector product of the radius- vector from the extremity of R to the extremity of A and the force.


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