The great Italian scientist and naturalist Galileo Galilei had a lasting historical influence on the development of not only specific sciences: physics, mechanics, astronomy, but also developed some fundamental principles for the development of science as a whole, the principle of Galileo's relativity, Galileo's transformations had a significant impact on the formation of the current picture of the world.
The scientific motive for Galileo's discovery of the principle of relativity was doubt in the correctness of formulas that reflect the acceleration of the motion of bodies. As you know, in the absence of acceleration in the movement of the system relative to some other reference frame, the acceleration of the body, relative to both of these systems, will be a constant value.
Since earlier, according to Newton’s laws, it was argued that it is acceleration that acts as the main parameter that describes the kinematics of bodies (Newton’s law 2), then forces can be dependent only on the position and velocity of bodies. Galileo questioned this dependence on the grounds that in this case all the equations of mechanics will take the same form in any of the reference systems. The statement that Galileo puts forward, the principle of relativity, argues that the laws of mechanics cannot depend on the system in which we study them. This principle can be more easily represented in action as follows.
For example, if you conduct an experiment simultaneously in two rooms, where one moves relative to the other, the result of our experiment will be the same for both rooms.
The requirements that Galileo formulated, the principle of relativity, were perceived as a postulate. Together with Newton’s laws, these conclusions of Galileo, as well as his transformation, had a significant impact on the development of mechanics as a science.
Galileo's transformations in the field of mechanics have also practically changed many of the previously prevailing ideas about mechanical processes. In particular, the laws of coordinate transformation that occur during the transition from one frame of reference to another assume the same time, and therefore the concept of "absolute time" is put forward. In this case, what Galileo claimed, the principle of relativity, acts as a special case of the Lorentz concept, and is applicable only for low speeds (relative to the speed of light, of course).
It should be said that before Galileo, physics was almost universally studied according to the works of Aristotle, they affirmed metaphysical ideas about nature and man. As far as physics is concerned, Aristotle, for example, argued that the rate of fall of a body is directly proportional to its weight and that any movement occurs only as long as it is influenced by a "motive." Galileo refuted these conclusions and formulated the correct ones, which reflect the true processes of falling and the dependence of speed on body weight during its movement.
The formulated mechanical principle of relativity of Galileo was first proposed in the book "Dialogue on the two systems of the world." In its simplest presentation, it sounds like this: for objects that move evenly, this movement does not affect only those objects that do not participate in this movement. This statement allowed the scientist to completely refute some of the postulates of astronomical heliocentrism, which stated that the very fact of the rotation of the Earth affects the course of events that occur on it.
What Galileo claimed, the principle of relativity, his mechanistic transformations, philosophical considerations became the basis for the discovery of many laws of physics after the death of the great scientist. These include, for example, the laws of energy conservation, the laws of the swing of the pendulum and the frequency distribution, he predicted and even introduced into circulation such a fundamental physical concept as the moment of force.