% PMe3201 - 2 2023
%
% Aula 02
% Exemplo de solucao da esfera com arrasto hidrodinamico
%
% Sao Paulo, 25.08.2023
% Walter Ponge-Ferreira

% Diagrama de derivadas no plano de fase
figure(1)
clf
[vx,vy] = meshgrid(-4:0.5:4,-2:0.5:6);
h = quiver(vx,vy,fx(vx,vy),fy(vx,vy));
xlabel('v_x')
ylabel('v_y')
title('Plano de Fase')
grid
shg

% Integracao Numerica
t=[0:0.01;10];
z0=[0,4,0,-2];
[t,z] = ode45('hidrodinamico',t,z0);
figure(2)
plot(z(:,2),z(:,4))
xlabel('v_x')
ylabel('v_y')
title('Trajetoria no Plano de Fase')
grid
shg

% Sobrepoem a trajetoria
figure(1)
hold on
plot(z(:,2),z(:,4))
shg

z0=[0,4,0,6];
[t,z] = ode45('hidrodinamico',t,z0);
plot(z(:,2),z(:,4))

z0=[0,-4,0,6];
[t,z] = ode45('hidrodinamico',t,z0);
plot(z(:,2),z(:,4))

z0=[0,-4,0,-2];
[t,z] = ode45('hidrodinamico',t,z0);
plot(z(:,2),z(:,4))


hold off

figure(2)
clf
plot(z(:,1),z(:,3))
xlabel('x(t)')
ylabel('y(t)')
title('Caminho da Esfera')
grid

% FIM