I'm currently being asked to write a state space model of a falling object (equation attached).
I had taken a linear systems course five years ago in which I did a lot of conversion between high order differential equations and systems of first order linear equations. However, this task seems odd for a few reasons:
Most nth ordered differential equations that I had converted only required n state variables. For example, if I had a second order differential equation, I needed two state variables. In this problem, it's asking for 3 state variable which seems odd. Is the third state variable even necessary?
This differential equation directly includes the independent variable (time) itself. It also includes an initial condition p0 which seems odd.
I'm able to derive a solution to this problem, however it just seems very odd in how I'm doing it. This is my solution: