Plotting solution to diff equation.
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I solved a system of differential equations using dsolve. In my solutions i got how my x,y and z variables behave,but I need to plot this as the position vector r=x+y+z through time. how do i get the input t into my solution soi can get a value for each point and plot my position.
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KSSV
2018-9-12
function botella_magnetica(a,k,m,q,x0,y0,z0,vx0,vy0,vz0)
x=x0;
y=y0;
z=z0;
vx=vx0;
vy=vy0;
vz=vz0;
V=[vx,vy,vz];
R=[x,y,z];
h=animatedline;
if abs(x0) > abs(a * 0.9)
disp('Fuera de zona de analisis')
return
end
grid on;
set(gca, 'XLim',[-100,100], 'YLim',[-100,100],'ZLim',[-100,100]);
k1 = (k * a^(3/2))/(((x+a)^2 + y^2 + z^2)^2);
k2 = (k * a^(3/2))/(((x-a)^2 + y^2 + z^2)^2);
Bx = ((x+a) * k1) - ((x-a) * k2);
By = (y * k1) - (y * k2);
Bz = (z * k1) - (z * k2);
B = [Bx,By,Bz];
Ac = (q/m).*(cross(V,B));
syms u(t) v(t) w(t);
eqn = [diff(u,t,2) == diff(v,t)*Bz - diff(w,t)*By, diff(v,t,2) == diff(w,t)*Bx - diff(u,t)*Bz, diff(w,t,2) == diff(u,t)*By - diff(v,t)*Bx];
Dx = diff(u,t); Dy = diff(v,t); Dz = diff(w,t);
cond = [u(0)==x0, v(0)==y0, w(0)==z0, Dx(0)==vx0, Dy(0)==vy0, Dz(0)==vz0];
sol = dsolve(eqn, cond);
u = sol.u ;
v = sol.v ;
w = sol.w ;
t = linspace(0,2*pi) ;
x = double(subs(u,t)) ;
y = double(subs(v,t)) ;
z = double(subs(w,t)) ;
display(sol);
plot3(x,y,z)
end
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