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?
B. What assumptions about the force must be made?
Newton's third law:
F12 = -F21
The Attempt at a Solution
I did the A. without a problem. It's the B. that troubles me a bit. I'm sure I'm missing what my prof wants me to find...
I wrote that the forces are equal and have opposite directions. The problem must lie on a single axis since there is only two particles. I'm not sure what other assumption we can make..
Thanks for the help!