Integration in Mechanics

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Integration in Mechanics

  1. A integrand with a singular point: using a limiting process or excluding a small sphere [Jack, p.36, (1.36); p.37, l.-4-l.-1].


  2. Evaluate the integral given in [Jack, p.60, (2.7)].
    Solution. Let x = cos g.  Then dx= -sin g dg.
    Let u = 1 + (a2/y2) and v = - (2a)/y.
    ò[0, p] cos g sin g (1 + (a2/y2) - (2a cos g )/y)-3 dg = ò[-1, 1] x (u + vx)-3 dx
    = v-2 ò[u-v, u+v] (z - u)z-3dz (Let z = u + vx).


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