Constructing the differential equation models of the physical systems by utilizing the physical laws of the process is very much important for analysis the characteristics and dynamic behavior of the system. Depending upon the system well known physical laws like Newton's law, Kirchhoff's laws etc. will be used to build mathematical models.
At First we build the physical model of the system as interconnection of idealized system elements and describe these in the form of elemental laws. These idealized elements are the building blocks of the system.
An ideal element is made by two basic assumptions
1. Spatial (relating to space) distribution of the element is ignored and it is consider as a point phenomen. As an example mass of a boby which has volume, is considered as concentrated at a poin.
2.Variables for the elements can be described by simple linear law of (i) a contant of proportionality or (ii) a first-order derivative or (iii) a first order integration.
To begin with consider an ideal elements which have a single port or two terminal representation so that two variable associated with it. These variables are identified as
1. Trrough variable VT
2. Across variable VA
Another classification of the element variables is
1. Input variable or independent variable(vi)
2. Output variable or dependent variable(V0)
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