With the double sum notation the kinetic energy simplifies to ft oo oc

J OO OO pi

1 fef fci


Because the mode shapes are orthogonal functions where f

J o mcpi (x )4>j(x) dx — | the total kinetic energy becomes

I oc

The "generalized equations of motion" can now be obtained by substitution of the kinetic energy ofEq. (2.105) and the potential energy ofEq. (2.99) into Lagrange's equations given as Eqs. (2.82). The resulting equations are then

0 0

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