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 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
′ M2 R
O The relevant relationships are: r1
= 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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- Fall '09
- external force