By Howard T. Odum
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Extra info for Energy Basis for Man and Nature
In this expression we have indicated explicit functional dependence only on those variables (i and x) that may be functions of time. 9) and expand the time derivative to obtain v = dJ, = 0), di + OA dx . 11) This expression illustrates some general terminal properties of magnetic 20 Lumped Electromechanical Elements field systems. 11) is proportional to di/dt and is the result of changing current. This term can exist when the system is mechanically stationary and is often referred to as a transformer voltage.
In order to obtain a representation for a mass element more general than a point mass, we need to review briefly the dynamics of rigid bodies. We consider first the translational motion of a rigid body. A rigid body, by definition, is one in which any line drawn in or on the body remains constant in length and all angles drawn in or on the body remain constant. In Fig. 12 we represent a rigid body with a mass density p (kilograms per cubic meter) that may vary from point to point in the body but remains constant in time at any point in the body.
Conventional circuit theory is the special case of stationary systems in which quasi-static electromagnetic field theory applies. All the concepts of circuit theory can be derived from field theoryt; for example, Kirchhoff's current law is derived from the conservation of charge. 1) where the surface S encloses the node. 2) where ik is the current flowing away from the node on the kth wire. Kirchhoff's voltage law is obtained by recognizing that a voltage is uniquely defined only in a region in which the time rate of change of magnetic flux density is negligible.
Energy Basis for Man and Nature by Howard T. Odum