# The Goddard Problem

The Goddard problem is the name for a simplified sounding rocket optimization problem. The problem is to find the optimal thrust curve for a vertical 1D rocket trajectory with a flat Earth, non varying gravity and simple v^{2} drag model with exponential decaying atmosphere in the form e^{-kh}.

## Setup

There are 3 state variables: distance from the center of the Earth *r*, velocity *v*, and mass *m*. We constrain ourselves to a line radial with Earth (along *r*) such that the problem becomes spatially one dimensional.