www.gusucode.com > stats 源码程序 matlab案例代码 > stats/PlotTrajectoriesOfABattedBaseballExample.m
%% Plot Trajectories of a Batted Baseball Using refcurve % Introduce the relevant physical constants. % Copyright 2015 The MathWorks, Inc. M = 0.145; % Mass (kg) R = 0.0366; % Radius (m) A = pi*R^2; % Area (m^2) rho = 1.2; % Density of air (kg/m^3) C = 0.5; % Drag coefficient D = rho*C*A/2; % Drag proportional to the square of the speed g = 9.8; % Acceleration due to gravity (m/s^2) %% % Simulate the trajectory with drag proportional to the square of the % speed, assuming constant acceleration in each time interval. dt = 1e-2; % Simulation time interval (s) r0 = [0 1]; % Initial position (m) s0 = 50; % Initial speed (m/s) alpha0 = 35; % Initial angle (deg) v0 = s0*[cosd(alpha0) sind(alpha0)]; % Initial velocity (m/s) r = r0; v = v0; trajectory = r0; while r(2) > 0 a = [0 -g] - (D/M)*norm(v)*v; v = v + a*dt; r = r + v*dt + (1/2)*a*(dt^2); trajectory = [trajectory;r]; end %% % Plot trajectory and use refcurve to add the drag-free parabolic % trajectory (found analytically) to the plot of trajectory. figure plot(trajectory(:,1),trajectory(:,2),'m','LineWidth',2) xlim([0,250]) h = refcurve([-g/(2*v0(1)^2),... (g*r0(1)/v0(1)^2) + (v0(2)/v0(1)),... (-g*r0(1)^2/(2*v0(1)^2)) - (v0(2)*r0(1)/v0(1)) + r0(2)]); h.Color = 'c'; h.LineWidth = 2; axis equal ylim([0,50]) grid on xlabel('Distance (m)') ylabel('Height (m)') title('{\bf Baseball Trajectories}') legend('With Drag','Without Drag')