Title: The Theory: Mechanics. An Example: Collision of a Point and a Plane
Abstract: Let us consider a point moving above an obstacle, for instance a plane. Neither of these two elements, the plane and the point, is deformable. But the system they form is deformable because the distance of the point to the plane changes. Based on this idea, a predictive theory of the motion is derived. Because the system is deformable, there exist internal forces. They are carefully introduced and investigated with their actual and virtual work. The theory gives important opening when describing the collisions. The duration of the collisions compared to the time flight is short. Thus we assume that the collisions are instantaneous. The development of the theory shows that this assumption is not restrictive and allows many opportunities. The collision equation of motion introduces an internal percussion which is given by a constitutive law. This constitutive law sums up the sophisticated and rapid evolutions occurring during the collisions. The constitutive laws allow for numerous physical behaviours. For instance, the theory predicts if a sheet of paper is transfixed by a falling steel ball. It gives also the velocity of the steel ball after the collision. This chapter gives the basic tools to investigate collisions of deformable solids, collisions of solids and fluids.
Publication Year: 2016
Publication Date: 2016-07-28
Language: en
Type: book-chapter
Indexed In: ['crossref']
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