Specifically, the term *Galilean invariance* today usually refers to this principle as applied to Newtonian mechanics, that is, Newton’s laws hold in all frames related to one another by a Galilean transformation. In other words, all frames related to one another by such a transformation are inertial (meaning, Newton's equation of motion is valid in these frames). In this context it is sometimes called *Newtonian relativity*.

Among the axioms from Newton's theory are:

Galilean relativity can be shown as follows. Consider two inertial frames *S* and *S'* . A physical event in *S* will have position coordinates *r* = (*x*, *y*, *z*) and time *t* in *S*, and *r'* = (*x'* , *y'* , *z'* ) and time *t'* in *S'* . By the second axiom above, one can synchronize the clock in the two frames and assume *t* = *t'* . Suppose *S'* is in relative uniform motion to *S* with velocity *v*. Consider a point object whose position is given by functions *r'* (*t*) *in* S' *and r*(*t*) in *S*. We see that

The velocity of the particle is given by the time derivative of the position:

Another differentiation gives the acceleration in the two frames:

This page was last edited on 8 November 2017, at 21:03 (UTC).

Reference: https://en.wikipedia.org/wiki/Galilean_relativity under CC BY-SA license.

Reference: https://en.wikipedia.org/wiki/Galilean_relativity under CC BY-SA license.

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- Galileo Galilei
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- Newtonian Mechanics
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- Galilean Relativity
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