The rolling tire interacts dynamically with the road surface, under the constant constraint of the load of vehicle. There are a bunch of distinct characteristics of this interaction, reflected in the friction force, for the case of traction and braking properties of the tire, in the noise produced by the tire when rolling, in the hydroplaning properties […]
From thermodynamical point of view the pressure is a stress, or a density of energy. The differential form thus defined by pressure should be a 3-form. As a matter of fact, the stresses in a material, in general, can be defined likewise, by a formula which generalizes only slightly the 3-form of pressure:
(1)
The origin of […]
The tire is a structure complicated not only by the details of design, but by the very physics involved in its working conditions. In the matters of tire design details, a century of designing and building tires has taught the manufacturers that the tires should have just about the same standard design features. The different […]
There are quite a few phenomena related to the theoretical physics of the tire that can be modeled by quadratic forms on its surface. First, one needs to account for the surfaces delimiting the tire. These are basically two: the internal surface of the carcass delimiting, together with the metallic part of the wheel (the […]
From a purely geometrical point of view, the variation of a quadratic form characterizing a surface cannot be assisted but by one of the two fundamental forms of that surface. This has a certain natural connotation, inasmuch as the quadratic forms that vary in this case are not any different from those ‘assisting’ that variation. […]
There is no general agreement as to what one should understand by “Cartan lemmas” or “Cartan theorems” when it comes to the development of the differential geometric concepts. As a matter of fact, as Robert Hermann says in his rich Addendum to the English version of Cartan’s Géométrie des Espaces de Riemann (Cartan, 1983), these […]