When modeling engineering systems, it can be difficult to identify the key parameters driving system behavior because they are often buried deep within the model. Analytical models can help because they describe systems using mathematical equations, showing exactly how different parameters affect system behavior.
In this article, we will derive analytical models of the loads and bending moments on the wing of a small passenger aircraft to determine whether the wing design meets strength requirements. We will derive the models in the notebook interface in Symbolic Math Toolbox™. We will then use the data management and analysis tools in MATLAB® to simulate the models for different scenarios to verify that anticipated bending moments are within design limits.
While this example is specific to aircraft design, analytical models are useful in all engineering and scientific disciplines –for example, they can be used to model drug interactions in biological systems, or to model pumps, compressors, and other mechanical and electrical systems.
By Dan Doherty, The MathWorks
This article was published in MATLAB Digest, July 2009.