Graphing second order differential equation

I am attemping to graph the solution to the following system of differential equations.
mx¨ = −C*x*sqrt(x˙^2 + y˙^2)
my¨ = −C*y* sqrt(x˙^2 + y˙^2)− mg
Initial conditions: x(0) = 0; y(0) = 0; C: 4*10^-7 (constant)
x˙ : first derivative of x position
x¨: second derivative of x position
y˙^2: square of first derivative of y position
I have tried the following code but I get an error message saying that the code attempts to graph the solution outside the defined range (5,5.8) although the equations describe the parabolic motion of an object acted on by a drag force and should be defined from x=0 to the range.
syms x(t) y(t)
t0 = 0;
tf = 5400;
dx=diff(x,t);
dy=diff(y,t);
eq1 = dx*sqrt((dx*dx +dy*dy)) == diff(x,2);
eq2 = dy*sqrt((dx*dx +dy*dy))-50 == 10*diff(y,2);
vars = [x(t); y(t)];
[V,S] = odeToVectorField([eq1,eq2])
M = matlabFunction(V,'vars', {'t','Y'});
interval = [t0 tf];
y0 = [0 0 0 1];
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1);
plot(tValues,yValues)

类别

在 帮助中心 和 File Exchange 中查找有关 Programming 的更多信息

回答:

ag
2025-3-12

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by