(Book: 5.2)
The momentum equation in words: the rate of change of momentum of a material region is the net force on the region:
Lagrangian formulation:
Note: by definition 
, so
we can also write this as 
.
Note: the book says the momentum equation above cannot be derived from
Newton's equation for a point mass. However, setting
for an infinitesimal element of
fluid with volume 
and integrating using action = -reaction
does produce the momentum equation above.
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