The internal dynamics of the system is given by the
acceleration a
of the relative position vector
r(t).
a =
d2r/dt2 =
d2r2/dt2 -
d2r1/dt2 =
a2 -
a1 =
=
(
F12 +
F2,ext
)/m2
-
(
F21 +
F1,ext
)/m1
Also using the definition
of the reduced mass,
we arrive at
μa =
F12 +
μ(
F2,ext
/m2 -
F1,ext
/m1
)
Hence, the acceleration
a
is determined by the force which mass
m1 exerts on mass
m2 and the reduced mass
μ,
except for a residual force which consists of the
external forces scaled by the
corresponding masses.
Some of the formulas are collected
here.
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