Graphing second order differential equation

Question

Aleem Andrew 2020-2-2

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https://ww2.mathworks.cn/matlabcentral/answers/503287-graphing-second-order-differential-equation

回答： ag 2025-3-12

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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)