# How to find the expression of the equation of the fundamental principle of dynamics starting from the Galileo group ?

+ 0 like - 0 dislike
3614 views
Good morning all,
I learned quite a while ago that the equation of the fundamental principle of
dynamics in Newtonian mechanics was discovered by studying its
invariance group which is the Galileo group.

In the beginning, physicists of the $17$ -th and $18$ -th century did not
yet know the notion of group as it is the case today, but did they nevertheless
extract the expression of the equation of the fundamental principle of
dynamics on the basis of the theoretical study of the relative movements of a
body moving in two Galilean frames of reference in motion of inertia.

Could you explain to me in details, how were they able to extract the
expression of the equation of the fundamental principle which is
$\sum \vec{F} = m \ \vec{a}$,
from its invariance group which is the Galilean group
$(\mathrm{SO} (3) \times \mathbb{R}^3) \times \mathbb{R}^4$?

Thanks in advance for your answers.


asked Nov 11, 2020
edited Nov 11, 2020

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysi$\varnothing$sOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). Please complete the anti-spam verification