Always start by making a drawing of the problem.
- Define the coordinate system (which way is positive/negative)
- What are the parts of the system and their interconnections/relationships (topology)
- Define variable quantities and names
For Kinetic/kinematic analysis, draw a free-body diagram of the system
- Label forces, displacements, angles, velocity vectors, acceleration vectors
- Check sign conventions on all parameters
Using your drawings, define mathematical relationships using the nomenclature and sign conventions from your drawing.
For a trajectory model, you will define the initial condition, then integrate the equations of motion over some period of time (i.e. a loop in the program), until some condition is reached (vertical position goes below the ground or time limit is reached - you need a mathematical expression for this condition). Use this condition to exit the loop.