Lecture Jan 22 2014

The comma in the subscript denotes partial

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Unformatted text preview: j 1,2,3 (for x, y, z) x j This is a vector equation in tensor notation. The comma in the subscript denotes partial differentiation as shown. In tensor notation two of the same subscript indices indicate summation over that index, whereas a single subscript remains as a “free” index indicating a vector. For example, bi is the vector for body force/unit mass at a point, for example gravity, acceleration effect, magnetic field, etc., which is more often not present. So for i=1, the expanded equation for the x‐ direction is as follows 11 21 21 xx yx zx b1 0 or bx 0 x1 x2 x3 x y z and similarly for the y and z equilibrium directions. 1 As shown subsequently in Section 2.7, applying moment equilibrium...
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