I have the following code:
t = 0:0.0001:20; %time
m = 0.4; %mass (kg)
g = 9.8; %gravitational accel. (m/s^2)
b = 0.44; %drag coefficient
w_1 = 10; %Angular Velocity
w_2 = 8; %Angular Velocityw_3 = 5; %Angular Velocityx_t_1 = (2349.*m)./(100.*b) - (2349.*m.*exp(-(b.*t)./m))./(100.*b);y_t_1 = (g.*m.*t.*w_1)./(b.^2 + w_1.^2) - (171.*b.^2.*m.*w_1)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (171.*m.*w_1.^3)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (2.*b.*g.*m.^2.*w_1)./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (171.*b.^3.*m.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*m.*w_1.^3.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.^2.*m.*w_1.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.*m.*w_1.^2.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) - (g.*m.^2.*w_1.^2.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (2.*b.*g.*m.^2.*w_1.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4);z_t_1 = (171.*b.^3.*m)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.*m.*w_1.^2)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (b.^2.*g.*m.^2)./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) - (g.*m.^2.*w_1.^2)./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) - (b.*g.*m.*t)./(b.^2 + w_1.^2) - (171.*b.^3.*m.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*m.*w_1.^3.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (171.*b.*m.*w_1.^2.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.^2.*m.*w_1.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (g.*m.^2.*w_1.^2.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (2.*b.*g.*m.^2.*w_1.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4);x_t_2 = (2349.*m)./(100.*b) - (2349.*m.*exp(-(b.*t)./m))./(100.*b);y_t_2 = (g.*m.*t.*w_2)./(b.^2 + w_2.^2) - (171.*b.^2.*m.*w_2)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (171.*m.*w_2.^3)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (2.*b.*g.*m.^2.*w_2)./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (171.*b.^3.*m.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*m.*w_2.^3.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.^2.*m.*w_2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.*m.*w_2.^2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) - (g.*m.^2.*w_2.^2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (2.*b.*g.*m.^2.*w_2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4);z_t_2 = (171.*b.^3.*m)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.*m.*w_2.^2)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (b.^2.*g.*m.^2)./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) - (g.*m.^2.*w_2.^2)./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) - (b.*g.*m.*t)./(b.^2 + w_2.^2) - (171.*b.^3.*m.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*m.*w_2.^3.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (171.*b.*m.*w_2.^2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.^2.*m.*w_2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (g.*m.^2.*w_2.^2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (2.*b.*g.*m.^2.*w_2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4);x_t_3 = (2349.*m)./(100.*b) - (2349.*m.*exp(-(b.*t)./m))./(100.*b);y_t_3 = (g.*m.*t.*w_3)./(b.^2 + w_3.^2) - (171.*b.^2.*m.*w_3)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (171.*m.*w_3.^3)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (2.*b.*g.*m.^2.*w_3)./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (171.*b.^3.*m.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*m.*w_3.^3.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.^2.*m.*w_3.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.*m.*w_3.^2.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) - (g.*m.^2.*w_3.^2.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (2.*b.*g.*m.^2.*w_3.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4);z_t_3 = (171.*b.^3.*m)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.*m.*w_3.^2)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (b.^2.*g.*m.^2)./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) - (g.*m.^2.*w_3.^2)./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) - (b.*g.*m.*t)./(b.^2 + w_3.^2) - (171.*b.^3.*m.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*m.*w_3.^3.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (171.*b.*m.*w_3.^2.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.^2.*m.*w_3.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (g.*m.^2.*w_3.^2.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (2.*b.*g.*m.^2.*w_3.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4);plot3(x_t_1, y_t_1, z_t_1)hold onplot3(x_t_2, y_t_2, z_t_2)plot3(x_t_3, y_t_3, z_t_3)xlabel('X')ylabel('Y')zlabel('Z')legend('\omega = 10 rad/s', '\omega = 8 rad/s', '\omega = 5 rad/s')hold off
I would like to shade the xy plane at z=0 to make the plot more visually appealing but I am not sure how to do this. I also only need the portion of each individual plot that appears before it goes below z=0 again. This plot is the trajectory of a soccer ball and at z=0 is the ground so mathematically the plots continue below z=0 but realistically this is not the case and I am not sure how to set this limit. Thank you in advanced for your help!
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