What is Galileon relativity?

Hint: Galileo di Vincenzo Bonaiuti de' Galilei, also known as Galileo di Vincenzo Bonaiuti de' Galilei, was an Italian astronomer, physicist, and engineer from Pisa. Galileo has been referred to as the "Father of Modern Astronomy," "Father of Modern Physics," "Father of the Scientific Method," and "Father of Modern Science."

Complete step by step solution:
The laws of motion are the same in all inertial frames, according to Galilean invariance or Galilean relativity. In his Dialogue Concerning the Two Chief World Systems, Galileo Galilei first described this principle in 1632, using the example of a ship traveling at a constant velocity, without rocking, on a smooth sea; any observer below the deck would be unable to tell whether the ship was moving or stationary.
According to Galilean relativity, all fundamental laws of physics are the same in all frames of reference that move at the same constant velocity. The Galilean principle states that inertial frames exist and that the same laws of physics apply to all inertial frames of reference, regardless of whether they move in a straight line or at a constant speed relative to one another.
The following diagram depicts Galilean relativity. Consider \[S\] and\[S'\], two inertial frames. A physical event \[S\] has position coordinates \[r\text{ }=\text{ }\left( x,\text{ }y,\text{ }z \right)\]and time\[t\], while a physical event in S' has position coordinates \[r'\text{ }=\text{ }\left( x',\text{ }y',\text{ }z'\text{ } \right)\]and time t'. The clocks in the two frames can be synchronized using the second axiom and \[t\text{ }=\text{ }t'\]can be assumed. Assume \[S'\] is moving \[v\] in a relatively uniform motion to\[S\]. Consider the position of a point object defined by the functions \[r'\text{ }\left( t \right)\]in \[S'\] and \[r\left( t \right)\]in S. We can see this,
\[{r}'(t)=r(t)-vt.\]
Thus, According to Galilean relativity, all fundamental laws of physics are the same in all frames of reference that move at the same constant velocity.

Note:
A Galilean group is a collection of motions that belong to Galilean relativity and act on the four dimensions of space and time to form Galilean geometry. In this description of uniform motion, Gailea formulated all of these Galilean transformation concepts.