ay45c4-page5 - we get  (M1 M2)R = 0 or R = 0 Thus the...

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Unformatted text preview: we get   (M1 + M2)R = 0 or R = 0 : Thus, the location of the center of mass of the system is unaccelerated, since there is no external force on the system. It follows that the center of mass moves at a constant velocity: R _ R  ddt = v = constant R = R0 + v 0 t : This relation expresses the \Conservation of Linear Momentum." R0 and V 0 are the rst 6 \constants of motion." The next logical thing to do is to change to center-of-mass coordinates r01; r02, that is, to coordinates relative to the center of mass. M1 CoM r1 ′ r1 r2 ′ M2 R r2 O The relevant relationships are: r1 r2 R = = = R + r01 R + r02 R0 + v0t : Substituting these into the equations of motion, we get  M r0 = GM1 M2 (r0 r0 ) 11 jr01 r02j3 64 1 2 ...
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