Physically Similar Systems: A History of the Concept is a chapter in the Springer Handbook of Model-Based Science by S. G. Sterrett. It is an interesting history. The principle behind similar systems is roughly that finding similar processes in similar systems can provide another tool for mathematical modeling. Dimensional analysis looks for mathematical modeling using basic quantities in a general sense such as length, time, mass, temperature, current, particle number, luminosity and so on. A criticism I found on the internet stated: the problem with similitude: it works in very much the same way as dimensional analysis, and can be used to derive many of the same results. The introduction of the idea as a new physical principle seems unnecessary and overly confusing. Do you agree with the critic? Or are there useful differences between dimensional analysis and the idea of physically similar systems?
I think we postulate the principle of similarity in order to perform dimensional analysis. In other words, to define dimensionless quantities, the system must be invariant with respect to its dimensions ( units ), that is, the dynamics can not depend on the dimensions of the system.
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