# Coordinate System

The first static equilibrium will be the forward surge of one meter per second. Compiling all of the forces and their respective direction on this axis.

Next to calculate the force needed from the thrusters is simply a sum of forces equation. This will give is the required.

Now here there is not a static equilibrium, so calculating how the thrust in the vertical and horizontal direction are calculated we take the sum of moments around the origin.

It is no concern to us that there is not a static equilibrium during the forward surge. This is because there is an altitude hold module that will keep the depth within a few centimeters, so the vertical thrusters will fire if the depth is not being held, and this is done automatically without the user input. Next, we need to make sure that there is a static equilibrium during a heath moment, this will be vital to us.

Doing a sum forces to determine the thrust needed.

This is extremely useful, since the motor we decide to use must have at least two kilograms of thrust. Now to take the sum of moments to determine the static equilibrium.

Bringing all of this together, we will have achieved static equilibrium for all cases.