Electromechanical Dynamics (Part 1).0093

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Lumped-Parameter Electromechanics From this expression we can now evaluate the mechanical forces of electric origin fl and f2 e (mechanical terminal relations); thus 8We 2 S 1 aS as 2 fie(ql, q 2 ,x1, x2) = - = -- q 1 2 -- q 1 q 2 S - 1q 2 2 , (e) w, 2 as asa a ass f 2 e(q 1 , q 2 , x1, x 2 ) = = -q 2 91q 2 a - q22 (f) Because S 1 , S 2, and S, are known as functions of zx and x 2 for this example, the derivatives in (e) and (f) can be calculated; this is straightforward differentiation, however, and is not carried out here. 3.1.2b Force-Coenergy Relations So far in the magnetic field examples the flux linkage A has been used as the independent variable, with current i described by the terminal relation. Similarly, in electric field examples charge q has been used as the independent variable, with voltage v described by the terminal relation. These choices were natural because of the form of the conservation of energy equations (3.1.9) and (3.1.13). Note that in Example 3.1.1 we were required to find vI(ql, q 2 ) and v,(ql, q 2 ).
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