Two Problems in Classical Mechanics

A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects. 1. Why Scaling, and why the given Groups ? Dimensional Analysis, Bluman & Kumei, is one of those fundamental aspects of Classical Physics which, nevertheless, is often left outside of one’s awareness, since it is taken so much for granted. What it says is that every measurable quantity, say X, in Classical Physics has the dimension, denoted by [X], given by a monomial (1.1) [X] = LMT γ where L, M and T are, respectively, length, mass and time, and they are the three Fundamental Mechanical Dimensions, while α, β, γ ∈ R are suitable exponents. For instance, in the case of velocity V , acceleration A, or energy E, we have, respectively, [V ] = LT, [A] = LT and [E] = LMT. It may, in view of its rather disregarded status, be surprising to see the extent to which the above concept of dimension is not trivial.