General mechanical engineering - Dynamics: classical shock theory

In many practical cases, the mechanical actions involved act for a very short time, but with a large amplitude. Consider an action . Its X, Y and Z components are shown in the figure below.

From the point of view of the fundamental law of mechanics, there is no change in nature. In practice, however, the difference is fundamental: from a physical point of view, it's very difficult to actually measure these mechanical actions.

In some cases, this has led to a formulation which, for the study of movements, makes it possible to dispense with actual knowledge of these actions. This is the classical theory of shock.

We shall see, moreover, that there is an important mathematical consequence. During this phase [t ₁ , t ₂ ], there will be a sudden variation in velocities, which we will treat mathematically as discontinuities. To find the motion at the end of this phase, we'll have to solve Cramer systems where the unknowns will be the velocity variations instead of having to find the solution of second-order differential equations, which explains the historical fact that shock theory was developed very early on.

Today, there is renewed interest in shock theory, due to the increasing speeds of means of locomotion and the sudden variations that can occur.

This is an important theory in all matters of safety and ball games.