Higher Order Systems
The general n-th order linear differential equation with constant coefficients has the form:
The function f(t) is known as the forcing function.
If the differential equation only contains real (not complex) coefficients, then the properties of such a system behaves as a mixture of first and second order systems only. This is because the roots of its characteristic polynomial are either real, or complex conjugate pairs. Therefore, understanding how nondimensionalization applies to first and second ordered systems allows the properties of higher order systems to be determined through superposition.
The number of free parameters in a nondimensionalized form of a system increases with its order. For this reason, nondimensionalization is rarely used for higher order differential equations. The need for this procedure has also been reduced with the advent of symbolic computation.
Read more about this topic: Nondimensionalization, Linear Differential Equations With Constant Coefficients
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