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Higher order equations in the construction of a dynamic system model

Lecture



If, when building a model of a dynamical system, it turned out that his records used derivatives of a second or more degree, this means that we are dealing with higher order equations. Higher order equations lead to a system of first order equations. Consider this by example.

Example 1. The following second order differential equation is given: y '' + y ' / x + y = 0. It is necessary to reduce it to a system of first order equations.

Denote: d y / d t = z ; d 2 y / d t 2 = z ' . Then: z ' + z / x + y = 0. And then we come to the system of differential equations of the first order:

  Higher order equations in the construction of a dynamic system model

Then we solve this system by means already known to us, for example, by the Euler method (see Lecture 10. Numerical methods for integrating differential equations. Euler method).


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System modeling

Terms: System modeling