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## Homework Statement

Consider Newton’s force law for two particles interact through a central force F12(r1',r2',u1,u2), where by Newton’s third law F12 = -F21.

m1(d^2r1/dt^2) = F12(r1,r2,u1,u2)

m2(d^2r2/dt^2) = F21(r1,r2,u1,u2)

A. Show that Newtonian mechanics is form invariant with respect to a Galilean transformation?

## Homework Equations

__Newton's third law__:

F12 = -F21

__Galilean Transform__:

t'=t

m'=m

r'=r-vt

## The Attempt at a Solution

I understand the concept of invariance. I understand Galilean relativity quite well. I just have no clue where to start the proof. I haven't done much proofs in my past physics and math courses.

I tried writing the two F=m*a equations with the primed coordinates but after that I'm lost. here is what I wrote:

m1(d^2(r1-v*t)/dt^2) = (F12)'((r1-v*t),(r2-v*t),(u1-v),(u2-v)

m2(d^2(r2-v*t)/dt^2) = -(F21)'((r1-v*t),(r2-v*t),(u1-v),(u2-v)