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Proving Newton's third law invariant with Galilean tranfrom
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[QUOTE="AllRelative, post: 4993531, member: 540873"] [h2]Homework Statement [/h2] 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? [h2]Homework Equations[/h2] [U]Newton's third law[/U]: F12 = -F21 [U]Galilean Transform[/U]: t'=t m'=m r'=r-vt [h2]The Attempt at a Solution[/h2] 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) [/QUOTE]
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Proving Newton's third law invariant with Galilean tranfrom
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