By Cliff Matthews
This is often an important convenient advisor containing precious brand new info usually wanted by means of the coed or practicing engineer. overlaying all features of plane, either fastened wing and rotary craft, this notebook presents easy accessibility to helpful aeronautical engineering info and resources of data for additional in-depth details.
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X p o s i t i v e ) X2 In (1 + x ) = x - - ~ - X3 X4 + ~-- ~ - + ... Trigonometric series X3 X5 5! X7 7! 6 7 + ... (x a < 1) 30 Aeronautical Engineer's Data Book tan-lx=x-lx3+5xS-- ~i X7 + ... 7 Vector algebra Vectors have direction and magnitude and satisfy the triangle rule for addition. Quantities such as velocity, force, and straight-line displacements may be represented by vectors. g. Ax, Ay, A z or Axi + A j + Azk. , is given by V = V 1 + V 2 ~- V 3 --}- . . )k Product of a vector V by a scalar quantity s sV = (sa)i + (sb)j + (sc)k (S 1 + s 2 ) V = S l Y + s2V ( V 1 + V2)s = V l S + V2s where sV has the same direction as V, and its magnitude is s times the magnitude of V.
All other elements are 0. The unit matrix is denoted by/. I= [ 0i] 1 0 Addition of matrices Two matrices may be added provided that they are of the same order. This is done by adding the corresponding elements in each matrix. al, a,2 a,3] + [b,l b,2 b,3] a21 a22 az3J [b21 b22 b23] = [all + b,l a12+ bl2 a13+ b13] [(/21 + b21 a22 + b22 a23 + b23] Subtraction of matrices Subtraction is done in a similar way to addition except that the corresponding elements are subtracted. al, al2] - [bl, b,2] a2~ a22J [al, - bll a,2-b12] [b2~ b22J = [ a21-b21 a22-b22J Fundamental dimensions and units 37 Scalar multiplication A matrix may b e multiplied by a n u m b e r as follows: b[all a12] [ball ba12] [a21 azzJ = [ba21 baz2J General matrix multiplication Two matrices c a n be multiplied together provided the n u m b e r of columns in the first matrix is equal t o the n u m b e r of rows in the second matrix.
It is d e n o t e d by: all a12 ... aln a21 a22 ... a2n aml am2 ... a rnn 36 Aeronautical Engineer's Data Book Square matrix This is a matrix having the same number of rows and columns. al, a12 a13] I a00] a21 a22 a23/ is a square matrix of order 3 × aBi a32 a33] 3. Diagonal matrix This is a square matrix in which all the elements are zero except those in the leading diagonal. 0a22 is a diagonal matrix of order 3 0 a33 × 3. Unit matrix This is a diagonal matrix with the elements in the leading diagonal all equal to 1.