Minimum problems in physics and economics

By minimum problems in general we will mean in the following all problems in which a certain quantity is stationary, leaving open whether a minimum (or a maximum) indeed occurs. The equations that provide the solution of the minimum problem (in the case of variation problems the so-called Euler's equations) depend, as to nature and form, on the function that becomes stationary.

The first chapter discusses some categories that can thus be distinguished, and gives some physical examples of each of them. From some of these categories so-called reciprocity relations can be deduced immediately; these relations are discussed more generally in the second chapter. Euler's equations can be brought into the so-called canonical form and Routh's form by introducing certain new change equations (“moments”). These transformations are discussed in the third chapter, then also giving minimum problems that directly yield these other equations as Euler's equations.

Tinbergen, J. (1929). Minimum problems in physics and economics. Dissertation, Leiden University.