The principle of relativity introduced by Galileo was primarily applied to mechanical systems. He said that no mechanical experiments allow us to determine whether the system is at rest or is moving in a straight and uniform manner. In other words, when performing identical mechanical experiments in various inertial coordinate systems (with acting inertia forces) , the results will be similar.
Galileo noticed that the mechanics of movements, or rather collisions, blows, projectile flight and other phenomena, give the same results: both in uniformly and rectilinearly moving laboratories, and in rest.
This mechanical principle of relativity can be explained using the following example. Suppose that one car drives next to another without any jerks, that is, at a constant speed, evenly. And everything around is shrouded in such dense dense fog that nothing is visible at all. The question is: can passengers in cars determine which one is moving? Can they be helped by experimenting in mechanics?
It turns out that in this case, passengers can observe only relative movement. Despite the fact that all the laws of motion and the rules of addition of vectors were developed with the help of moving laboratories, they do not detect, "do not feel" any influence of this movement on themselves. The principle of relativity also indicates that no mechanical experiments will detect the rectilinear uniform motion of the frame of reference relative to the stars and the Sun. However, with accelerated motion of the reference frame relative to the stars and the Sun, the experimental results are affected.
The Galilean principle of relativity in mechanics deserves special attention. None of the Galilean systems can be preferred in principle, despite the fact that from a practical point of view it is advisable to consider this or that reference frame preferable depending on the situation.
So, for a passenger traveling in a car, the coordinate system that is connected to the car will be a more natural frame of reference than that associated with the road. And the latter system, in turn, will become more convenient for a person watching the movement of a car, standing near the road. Different Galilean systems have fundamental equivalence, which is expressed in the fact that for the transition between the systems there are the same formulas, and only the relative speed value acts as a variable.
This principle of relativity is considered from the point of view of kinematics, however, similar equivalence of various systems is also characteristic of dynamics. This is the classical principle of relativity.
There is also a special principle that applies to any physical phenomena, and not just mechanical movements. Its essence lies in the fact that for any coordinate systems that move uniformly and rectilinearly relative to each other, any physical phenomena proceed the same way, and any physical experiments give a similar result.
This provision is defined as a special principle of relativity, since it applies to special cases of rectilinear uniform motion. In this case, all the laws look the same for the coordinate systems related to the stars, and for any other systems that move uniformly and rectilinearly relative to the stars.
There is also a more general principle that covers cases of coordinate systems with accelerated motion. It is called the general principle of relativity.