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?
Newton's third law:
F12 = -F21
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)