matlab二维轨迹图,matlab绘制抛物线轨迹

前文已经学会了语法和绘图函数，今天学习一个综合练习。

预备知识：高中小球斜抛的物理知识

代码如下：

%Purpose:

%This program calculates the distance traveled by a ball throw at a

%specified angle "theta" and a spedified velocity "vo" from a

%point,ignoring air friction.It calculates the angle yielding maximum

%range,and also plots selected trajectories.

%

%Define variable:

%conv Degrees to adians conv factor

%grav The gravity acceleration

%ii,jj Loop index

%index The maximum range in array

%maxangle The angle that gives the maximum range

%maxrange Maximum range

%time Time

%theta Initial angle

%fly_time The total trajectory time

%vo The initial velocity

%vxo x-component of the initial velocity

%vyo y-component of the initial velocity

%x x position of ball

%y y position of ball

%定义常数数值

conv=pi/180;

grav=-9.82;

vo=input('Enter the initial velocity:');

range=zeros(1,91);

%计算最大水平距离

for ii = 1:91

theta = ii -1;

vxo = vo * cos(theta * conv);

vyo = vo * sin(theta * conv);

max_time = -2 * vyo/grav;

range(ii) = vxo * max_time;

end

%显示计算水平距离的列表

fprintf('Angle versus Range\n');

for ii = 1:5:91

theta = ii-1;

fprintf('%2d\t\t%8.4f\n',theta,range(ii));

end

%计算最大的角度和水平距离

[maxrange,index]=max(range);

maxangle = index -1;

fprintf('\n Max range is %8.4f at %2d degrees.\n',maxrange,maxangle);

%绘制轨迹图形

for ii = 5:10:80

theta =ii;

vxo = vo*cos(theta*conv);

vyo = vo*sin(theta*conv);

max_time = -2 * vyo/grav;

%计算小球轨迹的x、y坐标数值

x=zeros(1,21);

y=zeros(1,21);

for jj=1:21

time = (jj-1) * max_time/20;

x(jj) = vxo * time;

y(jj) = vyo * time + 0.5 * grav * time^2;

end

plot(x,y,'g');

if ii == 5

hold on;

end

end

%添加图形的标题和坐标轴名称

title('\bf Trajectory of Ball vs Initial Angle \it\theta');

xlabel('\bf\itx\rm\bf(meters)');

ylabel('\bf\ity\rm\bf(meters)');

axis([0,max(range)+5,0,-vo^2/2/grav]);

grid on;

%绘制最大水平的轨迹图形

vxo = vo * cos(maxangle * conv);

vyo = vo * sin(maxangle * conv);

max_time = -2 * vyo/grav;

%计算(x,y)点

x = zeros(1,21);

y = zeros(1,21);

for jj = 1:21

time = (jj -1)*max_time/20;

x(jj) = vxo * time;

y(jj) =vyo * time + 0.5 * grav * time ^ 2;

end

plot(x,y,'r','Linewidth',2);

hold off;

将上述代码保存为ball.m,在matlab的命令窗口，输入ball后回车。输入不同的初始速度。运行情况如下：

>> ball

Enter the initial velocity:45

Angle versus Range

0 0.0000

5 35.8083

10 70.5286

15 103.1059

20 132.5504

25 157.9674

30 178.5847

35 193.7757

40 203.0790

45 206.2118

50 203.0790

55 193.7757

60 178.5847

65 157.9674

70 132.5504

75 103.1059

80 70.5286

85 35.8083

90 0.0000

Max range is 206.2118 at 45 degrees.

抛物线如下：

Vo为45m/s的抛物线.png

下面对ball.m中一些代码做一点解释：

zeros(1,91) 生成1*91的零矩阵

xlabel('\bf\itx\rm\bf(meters)')

\bf表示后边字符为黑体

\it表示后边字符为斜体

\rm恢复正常字体

hold off 方便下次调用ball.m时擦除前面的figure

练习：

1.对每个角度的抛物线用不同的颜色绘制，并用图例(legend函数)标注

2.绘制同样抛射角，不同初速度的图像