ABSTRACT
Analytic mechanics is a mathematical science, but it is of high importance for engineers as it provides analytic solutions to fundamental problems of engineering mechanics. The two analytic elasticity examples presented so far were one- and two-dimensional, respectively. The additional dimensions were negligible and ignored in the presentation. The chapter addresses the phenomenon of the bending of a beam with a non-negligible cross-section and consider all three dimensions. The physical components of the heat equation are of different dimensions. The transformation process is in essence the removal of dimensions from the physical equation by a specific normalization. The general solution of the differential equation will also be obtained with the same separation process but with different results due to the different boundary conditions.
