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L. Cveticanin and D. Cveticanin
Assuming that all bodies during mass separation belong to a unique system
(Fig. 1), we obtain the linear momentums K b before and K a after body separation.
Linear momentum before mass variation is equal to linear momentum of the initial
body
K b = K = Mv S
(4)
while the linear momentum after separation is a sum of the linear momentum which
corresponds to the separating mass (2) and linear momentum of the remaining mass
(3)
K a = K 1 + K 2 = mv S2 + (M − m)v S1
(5)
Difference between the linear momentums K a and K b during mass separation is
K = K a − K b = M(v S1 − v S ) − m(v S1 − v S2 )
(6)
Using the principle of linear momentum
K = F r t
(7)
where F r is the resultant external force acting during the time t, it yields
K ≡ M(v S1 − v S ) − m(v S1 − v S2 ) = F r t.
(8)
2.2 Principle of Angular Momentum
The angular momentum of the initial body with respect to the fixed point O is (see
Fig. 1)
L Ob = r S × Mv S + L S
(9)
where r S , v S , L S are the position vector, velocity and angular momentum of the mass
center S, respectively. If the angular momentum of the separating body is
L O2 = r S2 × mv S2 + L S2
(10)
where r S2 , v S2 , L S2 are the position vector, velocity and angular momentum of the
mass center S 2 , respectively, and of the remaining body relating to the fixed point O
is
L O1 = r S1 × (M − m)v S1 + L S1
(11)