I have calculated formulas with 1 dimensional trajectory motion (free-fall) including quadratic drag, and have created the following equations.
These equations of motion are not of much use on its own, therefore I would like either a analytical method/numerical method in order to plot 2-dimensional projectile motion on a graph, y against x. However, I am aware that the equations of motion for two-dimensional projectiles are the following: $$m*a_x=-k*\sqrt{v_x^2+v_y^2}*v_x$$ $$m*a_y=-mg-k*\sqrt{v_x^2+v_y^2}*v_y$$ I have realized that due to the formulas having a circular reference, there will be no general solution, hence there is no analytical method to plot this graph, as the drag in the x-direction will slow down the projectile and will change the drag in the y-direction as well as vise-versa.
Hence, this is where I do not know the approach to the problem, I am not very familiar with numerical methods of solving equations. Is there any way to do this in a spreadsheet or in MATLAB, maintaining a great level of accuracy (If possible, using RK4).
Note: x-velocity is oriented on the right hand side, and the y-velocity directly upwards.
Please correct me if I have made any mistakes.
velocity verlet
andverlet velocity
at this site. there are many answers that talk about it, and it's much easier to implement than RK4. Wikipedia also has info about it. $\endgroup$