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

- 522 + AOC , where 2 is a scalar, whose physical interpretation should be given.

33) at any instant. Now if a is a vector which varies with time, then there are matrices a = a2 a3} and de = {dc, Cx2(5C3) obtained by differentiating the resolutes. If the frame Ox1 x2 x3is fixed, we regard a as the matrix whose elements are the resolutes of d a/dt in Oxi x2 x3. To an observer moving with 0$1e2 e3 the matrix acan be regarded as the resolutes, in the frame O 1 e2 e3, of a vector we call a a/at. :• 8] 29 KINEMATICS IN THREE DIMENSIONS of the frame in obtaining the vector a ale t, which has the resolutes de = {a1 a2 6c3} in the frame OBI 2 3.

23), none of the resolutes {co, co, co,} or 421 Q2 Q3} is the time derivative of a single angle. In general, there is no angle which can be constructed whose rate of increase is col , or 0,, etc. ) When the phrase "the angular velocity of a body about an axis" is used, it is to be interpreted as the resolute of co along that axis. When speaking of linear motion we usually keep the word velocity for the vector and use the word speed or velocity component for the magnitude or resolute of the vector.

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