% Problème 9.5a

Variable x'',y'', theta'

Constant vb = 15 m/s 

% First two equations are the velocity expressions
eq[1]=-x'+vb*cos(theta)
eq[2]=-y'+vb*sin(theta)-(0.1+0.098*x-0.00049*x^2)
% Third equation is the constraint
eq[3]=1/4-y'/x'

% We want to solve for x'(x=0), y'(x=0), theta(x=0)
% Those are the initial conditions
SolveSetInput(Evaluate(eq,x=0), x'=1 m/s,y'=1 m/s,theta=13 deg)
% Important to use solvesetinput instead of solve:
%   (solve set x', y' and theta to constants values)... 

% - We could keep solving the non-linear equations for x', y' and theta 
%     at each timestep and integrate forward to find x and y. 
% - However, the non-linear solver takes a long time to run
% - Instead, we differentiate the equations to get ODEs that 
%     are linear in x'', y'' and theta'. With the right initial conditions found
%     previously, we can integrate forward for x', y', x, y and theta. That is FAST!

% Initial x and y conditions
Input x=0 m,y=0 m
% Integrate until the given stop time, if we have x = 200 and y = 50 then we are good!
Input tfinal=15.025 sec

Output t sec, x m , y m, x' m/s, y' m/s, theta deg

% Integrate the derivative of the equations
ODE(dt(eq), x'',y'',theta')