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Q˙m , φm+1 , . . φn , φ˙ m+1 , . . φ˙ n ) ik = d dt ∂L ∂ q˙j − d dt ∂L ∂ φ˙ k − (1) ∂L j = 1, . . m ∂qj ∂L k = m + 1, . . n ∂φk Note that, although the theory is presented here in the context of n-ports, it can equally be applied to (n + 1)-terminal elements. Some examples of Lagrangian n-ports are as follows: Example 1. A Lagrangian of the form L(q1 ) gives v1 = Example 3. A Lagrangian of the form L = f1 (q1 )+ f2 (q˙1 ) gives v1 = for some partition {1, . . m} and {m + 1, . . n} of the ports.

36 37 39 40 velocities η˙ i (and possibly time) from which the dynamical equations of the system can be derived. The application of this concept in the context of circuit theory had been studied by a number of authors in the middle decades of the last century, and this work was significantly advanced by Chua in papers such as [4, 8]. Chua presented an introduction to the properties of circuit elements characterized by a Lagrangian in his graduate courses in the University of California, Berkeley, and in a number of keynote addresses, but did not include it in any of his textbooks.

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A Nonstationary Model of the Universe


by William
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