[Unified-mailman] Systems Lab 4

[Mark Drela]

>I had a few questions about the Systems Lab 4 assignment.  
>In the part where we analyze stage 2 and 3, it asks us to find 
>the exit velocity of the rocket and the thrust.  I worked them 
>both out and found exit velocity and thrust as dependent 
>on volume of air.  However, volume of air is dependent on 
>time and exit velocity.  
>So when I plug the equation for volume into exit velocity 
>and try to solve for exit velocity as a function of time, 
>I get an extremely complicated equation that would take 
>a very long time to solve.

The volume of air at any time level is an auxilliary quantity 
which is a function of only the state variables at that same time level.  
In particular, the air volume depends on the water mass, which in turn
depends on the total mass state variable m_i.

There's no need to solve differential equations for the air volume,
or whatever you are trying to do.

MD