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    readme.md

    物理曲线的Pytthon绘制

    所需Lib

    1. matplotlib
    2. numpy

    所绘制曲线

    1. 重力势能曲线
    2. 抛体运动曲线
    3. 点电荷电力线分布
    4. 电偶极子电力线和等势面分布
    5. 简谐振动
    6. 李萨如图形

    代码实现

    #coding:utf-8
    import numpy as np
    import matplotlib.pyplot as plt
    
    # 支持中文
    plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
    
    
    # 控制图形的长和宽单位为英寸,
    # 调用figure创建一个绘图对象,并且使它成为当前的绘图对象。
    plt.figure(figsize=(5,5))
    # 设置X轴的范围
    plt.xlim(0,10)
    # 设置Y轴的范围
    plt.ylim(0,100)
    
    # 曲线设置
    x=np.linspace(0,10,10)
    y=np.array(9.8*x)
    
    #$可以让字体变得跟好看
    #给所绘制的曲线一个名字,此名字在图示(legend)中显示。
    # 只要在字符串前后添加"$"符号,matplotlib就会使用其内嵌的latex引擎绘制的数学公式。
    #color : 指定曲线的颜色
    #linewidth : 指定曲线的宽度
    plt.plot(x,y, '--c',marker='o',label="$9.8*x$",color="red",linewidth=2, markersize=5)
    #设置X轴的文字
    plt.xlabel("High(下落高度)")
    #设置Y轴的文字
    plt.ylabel("Ep(重力势能)")
    #设置图表的标题
    plt.title("重力势能曲线")
    
    
    #显示图示
    plt.legend()
    #显示出我们创建的所有绘图对象。
    plt.show()
    import numpy as np
    import matplotlib.pyplot as plt
    
    def projectile(V_initial, theta, bouyancy=True, drag=True):
        g = 9.81
        m = 1
        C = 0.47
        r = 0.5
        S = np.pi*pow(r, 2)
        ro_mars = 0.0175
    
        time = np.linspace(0, 100, 10000)
        tof = 0.0
        dt = time[1] - time[0]
        bouy = ro_mars*g*(4/3*np.pi*pow(r, 3))
        gravity = -g * m
        V_ix = V_initial * np.cos(theta)
        V_iy = V_initial * np.sin(theta)
        v_x = V_ix
        v_y = V_iy
        r_x = 0.0
        r_y = 0.0
        r_xs = list()
        r_ys = list()
        r_xs.append(r_x)
        r_ys.append(r_y)
        # This gets a bit 'hand-wavy' but as dt -> 0 it approaches the analytical solution.
        # Just make sure you use sufficiently small dt (dt is change in time between steps)
        for t in time:
            F_x = 0.0
            F_y = 0.0
            if (bouyancy == True):
                F_y = F_y + bouy
            if (drag == True):
                F_y = F_y - 0.5*C*S*ro_mars*pow(v_y, 2)
                F_x = F_x - 0.5*C*S*ro_mars*pow(v_x, 2) * np.sign(v_y)
            F_y = F_y + gravity
    
            r_x = r_x + v_x * dt + (F_x / (2 * m)) * dt**2
            r_y = r_y + v_y * dt + (F_y / (2 * m)) * dt**2
            v_x = v_x + (F_x / m) * dt
            v_y = v_y + (F_y / m) * dt
            if (r_y >= 0.0):
                r_xs.append(r_x)
                r_ys.append(r_y)
            else:
                tof = t
                r_xs.append(r_x)
                r_ys.append(r_y)
                break
    
        return r_xs, r_ys, tof
    
    v = 30
    theta = np.pi/4
    
    fig = plt.figure(figsize=(8,4), dpi=100)
    r_xs, r_ys, tof = projectile(v, theta, True, True)
    plt.plot(r_xs, r_ys, 'g:', label="Gravity, Buoyancy, and Drag")
    r_xs, r_ys, tof = projectile(v, theta, False, True)
    plt.plot(r_xs, r_ys, 'b:', label="Gravity and Drag")
    r_xs, r_ys, tof = projectile(v, theta, False, False)
    plt.plot(r_xs, r_ys, 'k:', label="Gravity")
    plt.title("Trajectory", fontsize=14)
    plt.xlabel("Displacement in x-direction (m)")
    plt.ylabel("Displacement in y-direction (m)")
    plt.ylim(bottom=0.0)
    plt.legend()
    plt.show()
    #coding:utf-8
    import numpy as np
    import matplotlib.pyplot as plt
    import math
    
    # 支持中文
    plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
    #显示负号
    plt.rcParams['axes.unicode_minus'] = False
    
    
    # 控制图形的长和宽单位为英寸,
    # 调用figure创建一个绘图对象,并且使它成为当前的绘图对象。
    plt.figure(figsize=(5,5))
    # 设置X轴的范围
    plt.xlim(-10,10)
    # 设置Y轴的范围
    plt.ylim(-10,10)
    
    # 曲线设置
    x=np.linspace(0,10,10)
    y=np.array(x)
    
    #$可以让字体变得跟好看
    #给所绘制的曲线一个名字,此名字在图示(legend)中显示。
    # 只要在字符串前后添加"$"符号,matplotlib就会使用其内嵌的latex引擎绘制的数学公式。
    #color : 指定曲线的颜色
    #linewidth : 指定曲线的宽度
    rad = 0
    for i in range(-50,50):
        y = math.tan(rad)*x
        rad += math.pi/6
        plt.plot(x,y, '--c',marker='^',color="red",linewidth=2, markersize=5)
        plt.plot(-x,y, '--c',marker='^',color="red",linewidth=2, markersize=5)
    plt.plot(0,0, '--c',marker='o',label="点电荷",color="blue",linewidth=2, markersize=15)
    #设置图表的标题
    plt.title("点电荷电力线分布")
    
    
    #显示图示
    plt.legend()
    #显示出我们创建的所有绘图对象。
    plt.show()
    from matplotlib.tri import (
      Triangulation, UniformTriRefiner, CubicTriInterpolator)
    import matplotlib.pyplot as plt
    import matplotlib.cm as cm
    import numpy as np
    
    #-----------------------------------------------------------------------------
    # Electrical potential of a dipole
    #-----------------------------------------------------------------------------
    def dipole_potential(x, y):
      """ The electric dipole potential V """
      r_sq = x**2 + y**2
      theta = np.arctan2(y, x)
      z = np.cos(theta)/r_sq
      return (np.max(z) - z) / (np.max(z) - np.min(z))
    
    #-----------------------------------------------------------------------------
    # Creating a Triangulation
    #-----------------------------------------------------------------------------
    # First create the x and y coordinates of the points.
    n_angles = 30
    n_radii = 10
    min_radius = 0.2
    radii = np.linspace(min_radius, 0.95, n_radii)
    
    angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
    angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
    angles[:, 1::2] += np.pi / n_angles
    
    x = (radii*np.cos(angles)).flatten()
    y = (radii*np.sin(angles)).flatten()
    V = dipole_potential(x, y)
    
    # Create the Triangulation; no triangles specified so Delaunay triangulation
    # created.
    triang = Triangulation(x, y)
    
    # Mask off unwanted triangles.
    triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
                 y[triang.triangles].mean(axis=1))
            < min_radius)
    
    #-----------------------------------------------------------------------------
    # Refine data - interpolates the electrical potential V
    #-----------------------------------------------------------------------------
    refiner = UniformTriRefiner(triang)
    tri_refi, z_test_refi = refiner.refine_field(V, subdiv=3)
    
    #-----------------------------------------------------------------------------
    # Computes the electrical field (Ex, Ey) as gradient of electrical potential
    #-----------------------------------------------------------------------------
    tci = CubicTriInterpolator(triang, -V)
    # Gradient requested here at the mesh nodes but could be anywhere else:
    (Ex, Ey) = tci.gradient(triang.x, triang.y)
    E_norm = np.sqrt(Ex**2 + Ey**2)
    
    #-----------------------------------------------------------------------------
    # Plot the triangulation, the potential iso-contours and the vector field
    #-----------------------------------------------------------------------------
    fig, ax = plt.subplots()
    ax.set_aspect('equal')
    # Enforce the margins, and enlarge them to give room for the vectors.
    ax.use_sticky_edges = False
    ax.margins(0.07)
    
    ax.triplot(triang, color='0.8')
    
    levels = np.arange(0., 1., 0.01)
    cmap = cm.get_cmap(name='hot', lut=None)
    ax.tricontour(tri_refi, z_test_refi, levels=levels, cmap=cmap,
           linewidths=[2.0, 1.0, 1.0, 1.0])
    # Plots direction of the electrical vector field
    ax.quiver(triang.x, triang.y, Ex/E_norm, Ey/E_norm,
         units='xy', scale=10., zorder=3, color='blue',
         width=0.007, headwidth=3., headlength=4.)
    
    ax.set_title('Gradient plot: an electrical dipole')
    plt.show()
    import matplotlib.pyplot as plt
    import numpy as np
    
    
    def f(t):
        return np.cos(2 * np.pi * t)
    
    
    a = np.arange(0.0, 5.0, 0.02)
    
    plt.plot(a, f(a))
    plt.xlabel('横坐标(时间)', fontproperties='Kaiti', fontsize=14, color='red')
    plt.ylabel('纵坐标(振幅)', fontproperties='SimHei', fontsize=18, color='red')
    plt.title('简谐运动 y=cos(2πx)', fontproperties='SimHei', fontsize=18, color='green')
    plt.grid(True)
    plt.axis([-1, 6, -2, 2])
    plt.annotate('简谐运动曲线', xy=(3, 1), xytext=(4, 1.5), arrowprops=dict(facecolor='black', shrink=0.2),
                 fontproperties='SimHei', fontsize=12, color='red')
    
    plt.show()
    import numpy as np
    from matplotlib.pyplot import plot
    from matplotlib.pyplot import show
    a = float(input())
    b = float(input())
    t = np.linspace(-np.pi, np.pi, 201)
    x = np.sin(a * t + np.pi/2)
    y = np.sin(b * t)
    plot(x, y)
    show()

    GITHUB链接

    东方怂天的GitHub

    项目简介

    自己绘制和网上收集的部分物理曲线的Python实现

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    开发语言

    • Python 100.0 %