The velocity of mass m1
follows from the time derivative of
r1(t).
The expression for r1(t)
in terms of the center-of-mass
position vector RCM(t)
and the relative position vector
r(t)
has been given at a previous page.
For its time derivative we find
dr1/dt
= dRCM/dt
- m2 ( dr/dt
) / (
m1 + m2
)
v1(t)
= VCM(t)
- m2 v(t)
/ (
m1 + m2
)
and, similarly, for mass m2
dr2/dt
= dRCM/dt
+ m1 ( dr/dt
) / (
m1 + m2
)
v2(t)
= VCM(t)
+ m1 v(t)
/ (
m1 + m2
)
VCM(t)
represents the velocity
of the center-of-mass with respect to the origin of
the coordinate system,
whereas v(t)
represents the velocity of mass m2
with respect to mass m1.
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