kill(all)$
load(lrats)$

equation of motion for variable mass ,version 1.0
peter.vlasschaert@gmail.com,16/07/2018

reason :  m=m(t),mass change in time.
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depends(m,t);

reason :  v=v(t),velocity change in time.
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depends(v,t);

linear momentum :  p=m*v= mass*velocity.
===================================

p1:p=m*v;

result : p=p(t)

depends(p,t);

F_v( = Force)= differentation,linear momentum with time
===============================================
rem : v = velocity

p2:diff(p1,t);

p3: F_v = rhs(p2);

p4:lhs(p3)=lhs(p2);

rem : Newton law for variable mass , p2,p3,p4

Motion of small mass ( = dm) exerted with velocity ( = u)
rem : dm lost of fuel.( = exerted mass)

T 1= rate of change of linear momentum (small mass)  => differentation
============================================
     =>   v = velocity ( pos : direction)  , v =reference.
     =>   u = velocity ( neg : direction)

p5:T_1= (v-u)*diff(m,t);

rem : T_1 => linear momentum = after - before = m*(v+dv) - u*dm

T2= rate of change of linear momentum (main body) => differentation
===========================================
     =>   v = velocity ( pos : direction)

p6:T_2=m*diff(v,t);

rem : T_2 => linear momentum = after -before = m*(v+dv) -m*v = m*dv

F = applied external force
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p7:F=rhs(p5)+rhs(p6);

u = 0  => F_v = F
=============

p8:subst([u=0,F=F_v],p7);

rem : same as , 'p4','p2','p3'.
=======================
u = exhausted of fuel gives changes of mass of the main body.