General mechanical engineering - General dynamics. Vector form

The dynamic part of classical mechanics is based on Newton's law, which is present in all its elements (mass, mechanical action, preferred reference frame, time). Dynamics aims to solve two problems:

• find the motion that any system takes when subjected to what we call mechanical actions;

• find the mechanical actions that will give any system a particular motion.

The fundamental law itself is not operational. There are two classic ways of obtaining operational tools. One is the method of general theorems, the other is analytical mechanics. In this article, following the fundamental law, we will develop the method of general theorems, which is characterized mainly by the following two elements:

• mechanical actions, represented by vectors called forces, which are treated using torsor theory;

• the laws of motion, translated into two vector theorems: the dynamic sum theorem and the dynamic moment theorem.

Each of these theorems translates into three scalar equations on appropriate axes.

Here, vector calculus is the most suitable form for presenting results, so this form of mechanics is sometimes referred to as vector mechanics.

However, a scalar theorem - the kinetic energy theorem - is classically attached to the general vector theorems. This very important theorem is considered a consequence of the general theorems.