{"id":1173895,"date":"2025-01-15T17:09:25","date_gmt":"2025-01-15T09:09:25","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1173895.html"},"modified":"2025-01-15T17:09:32","modified_gmt":"2025-01-15T09:09:32","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e5%81%9a%e7%89%a9%e7%90%86%e4%bb%bf%e7%9c%9f","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1173895.html","title":{"rendered":"\u5982\u4f55\u7528python\u505a\u7269\u7406\u4eff\u771f"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/26075537\/9e889ed9-4e73-415d-99f6-2bba843055e4.webp\" alt=\"\u5982\u4f55\u7528python\u505a\u7269\u7406\u4eff\u771f\" \/><\/p>\n<p><p> <strong>\u4f7f\u7528Python\u8fdb\u884c\u7269\u7406\u4eff\u771f\u7684\u6838\u5fc3\u5728\u4e8e\u7075\u6d3b\u8fd0\u7528\u79d1\u5b66\u8ba1\u7b97\u5e93\u3001\u6570\u503c\u65b9\u6cd5\u3001\u4ee5\u53ca\u7269\u7406\u5b66\u57fa\u672c\u539f\u7406\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u5e38\u7528\u7684\u65b9\u6cd5\u548c\u5e93\uff1aNumPy\u3001SciPy\u3001Matplotlib\u3001SymPy\u3001PyBullet\u3001Pygame<\/strong>\u3002\u8fd9\u4e9b\u5de5\u5177\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u5b9e\u73b0\u7269\u7406\u4eff\u771f\u7684\u57fa\u7840\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5176\u4e2d\u4e00\u4e2a\u5e93\u7684\u4f7f\u7528\uff0c\u5373NumPy\u3002<\/p>\n<\/p>\n<p><p>NumPy\u662fPython\u4e2d\u5904\u7406\u6570\u7ec4\u548c\u77e9\u9635\u8fd0\u7b97\u7684\u5e93\uff0c\u63d0\u4f9b\u4e86\u8bb8\u591a\u9ad8\u7ea7\u7684\u6570\u5b66\u51fd\u6570\u3002\u5047\u8bbe\u6211\u4eec\u8981\u6a21\u62df\u4e00\u4e2a\u7b80\u5355\u7684\u7269\u7406\u73b0\u8c61\uff0c\u5982\u81ea\u7531\u843d\u4f53\u8fd0\u52a8\u3002\u81ea\u7531\u843d\u4f53\u8fd0\u52a8\u7684\u57fa\u672c\u65b9\u7a0b\u5f0f\u662f\uff1as = ut + 1\/2at^2\uff0c\u5176\u4e2ds\u662f\u4f4d\u79fb\uff0cu\u662f\u521d\u901f\u5ea6\uff0ca\u662f\u52a0\u901f\u5ea6\uff0ct\u662f\u65f6\u95f4\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528NumPy\u6765\u8ba1\u7b97\u7269\u4f53\u5728\u4e0d\u540c\u65f6\u95f4\u70b9\u7684\u4f4d\u79fb\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001NUMPY\u5e93\u7684\u57fa\u7840\u4ecb\u7ecd<\/h3>\n<\/p>\n<p><p>NumPy\uff08Numerical Python\uff09\u662f\u4e00\u4e2a\u5f00\u6e90\u7684Python\u5e93\uff0c\u4e3b\u8981\u7528\u4e8e\u8fdb\u884c\u79d1\u5b66\u8ba1\u7b97\u3002\u5b83\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f3a\u5927\u7684N\u7ef4\u6570\u7ec4\u5bf9\u8c61\uff0c\u4ee5\u53ca\u8bb8\u591a\u7528\u4e8e\u64cd\u4f5c\u8fd9\u4e9b\u6570\u7ec4\u7684\u51fd\u6570\u3002NumPy\u7684\u6838\u5fc3\u662f\u5176\u5f3a\u5927\u7684\u591a\u7ef4\u6570\u7ec4\u5bf9\u8c61<code>ndarray<\/code>\uff0c\u5b83\u5141\u8bb8\u5bf9\u5927\u6570\u636e\u96c6\u8fdb\u884c\u9ad8\u6548\u64cd\u4f5c\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u5b89\u88c5NumPy<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86NumPy\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">pip install numpy<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001NumPy\u6570\u7ec4<\/h4>\n<\/p>\n<p><p>NumPy\u6570\u7ec4\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u591a\u7ef4\u6570\u7ec4\u5bf9\u8c61\u3002\u4e0ePython\u5185\u7f6e\u7684\u5217\u8868\u4e0d\u540c\uff0cNumPy\u6570\u7ec4\u53ef\u4ee5\u8fdb\u884c\u77e2\u91cf\u5316\u64cd\u4f5c\uff0c\u4ece\u800c\u5927\u5927\u63d0\u9ad8\u4e86\u8ba1\u7b97\u6548\u7387\u3002\u4f8b\u5982\uff0c\u4e0b\u9762\u662f\u4e00\u4e2a\u7b80\u5355\u7684NumPy\u6570\u7ec4\u793a\u4f8b\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u521b\u5efa\u4e00\u4e2a\u4e00\u7ef4\u6570\u7ec4<\/strong><\/h2>\n<p>a = np.array([1, 2, 3, 4, 5])<\/p>\n<h2><strong>\u521b\u5efa\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4<\/strong><\/h2>\n<p>b = np.array([[1, 2, 3], [4, 5, 6]])<\/p>\n<p>print(a)<\/p>\n<p>print(b)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e8c\u3001NUMPY\u5728\u7269\u7406\u4eff\u771f\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n<p><p>NumPy\u4e0d\u4ec5\u53ef\u4ee5\u8fdb\u884c\u57fa\u672c\u7684\u6570\u7ec4\u64cd\u4f5c\uff0c\u8fd8\u53ef\u4ee5\u7528\u4e8e\u66f4\u590d\u6742\u7684\u7269\u7406\u4eff\u771f\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528NumPy\u8fdb\u884c\u81ea\u7531\u843d\u4f53\u8fd0\u52a8\u7684\u4eff\u771f\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u81ea\u7531\u843d\u4f53\u8fd0\u52a8\u4eff\u771f<\/h4>\n<\/p>\n<p><p>\u81ea\u7531\u843d\u4f53\u8fd0\u52a8\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u7269\u7406\u73b0\u8c61\uff0c\u63cf\u8ff0\u4e86\u7269\u4f53\u5728\u91cd\u529b\u4f5c\u7528\u4e0b\u81ea\u7531\u4e0b\u843d\u7684\u8fc7\u7a0b\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528NumPy\u6765\u6a21\u62df\u8fd9\u4e00\u8fc7\u7a0b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<h2><strong>\u5b9a\u4e49\u521d\u901f\u5ea6\u3001\u52a0\u901f\u5ea6\u548c\u65f6\u95f4\u6570\u7ec4<\/strong><\/h2>\n<p>u = 0  # \u521d\u901f\u5ea6<\/p>\n<p>a = 9.8  # \u91cd\u529b\u52a0\u901f\u5ea6<\/p>\n<p>t = np.linspace(0, 10, 100)  # \u65f6\u95f4\u6570\u7ec4\uff0c\u4ece0\u523010\u79d2\uff0c\u5206\u6210100\u4e2a\u70b9<\/p>\n<h2><strong>\u8ba1\u7b97\u4f4d\u79fb<\/strong><\/h2>\n<p>s = u * t + 0.5 * a * t2<\/p>\n<h2><strong>\u7ed8\u5236\u4f4d\u79fb-\u65f6\u95f4\u56fe<\/strong><\/h2>\n<p>plt.plot(t, s)<\/p>\n<p>plt.xlabel(&#39;Time (s)&#39;)<\/p>\n<p>plt.ylabel(&#39;Displacement (m)&#39;)<\/p>\n<p>plt.title(&#39;Free Fall Motion&#39;)<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528NumPy\u7684<code>linspace<\/code>\u51fd\u6570\u751f\u6210\u4e86\u4e00\u4e2a\u4ece0\u523010\u79d2\u7684\u65f6\u95f4\u6570\u7ec4\uff0c\u7136\u540e\u6839\u636e\u81ea\u7531\u843d\u4f53\u8fd0\u52a8\u7684\u65b9\u7a0b\u8ba1\u7b97\u4e86\u6bcf\u4e2a\u65f6\u95f4\u70b9\u7684\u4f4d\u79fb\u3002\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528Matplotlib\u5e93\u7ed8\u5236\u4e86\u4f4d\u79fb-\u65f6\u95f4\u56fe\u3002<\/p>\n<\/p>\n<p><h3>\u4e09\u3001SCIPY\u5e93\u7684\u9ad8\u7ea7\u5e94\u7528<\/h3>\n<\/p>\n<p><p>SciPy\uff08Scientific Python\uff09\u662f\u4e00\u4e2a\u57fa\u4e8eNumPy\u7684\u5f00\u6e90Python\u5e93\uff0c\u63d0\u4f9b\u4e86\u8bb8\u591a\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97\u7684\u9ad8\u7ea7\u51fd\u6570\u3002SciPy\u5305\u62ec\u4e86\u8bb8\u591a\u5b50\u6a21\u5757\uff0c\u5982\u7ebf\u6027\u4ee3\u6570\u3001\u79ef\u5206\u3001\u4f18\u5316\u3001\u63d2\u503c\u7b49\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u5b89\u88c5SciPy<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86SciPy\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">pip install scipy<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001SciPy\u5728\u7269\u7406\u4eff\u771f\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n<p><p>SciPy\u63d0\u4f9b\u4e86\u8bb8\u591a\u9ad8\u7ea7\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u66f4\u590d\u6742\u7684\u7269\u7406\u4eff\u771f\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528SciPy\u8fdb\u884c\u7b80\u5355\u8c10\u632f\u5b50\u7684\u4eff\u771f\u3002<\/p>\n<\/p>\n<p><h3>\u56db\u3001SIMPLE HARMONIC OSCILLATOR (SHO)\u4eff\u771f<\/h3>\n<\/p>\n<p><p>\u7b80\u5355\u8c10\u632f\u5b50\u662f\u53e6\u4e00\u4e2a\u7ecf\u5178\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u63cf\u8ff0\u4e86\u4e00\u4e2a\u4ee5\u56fa\u5b9a\u9891\u7387\u632f\u8361\u7684\u7269\u4f53\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528SciPy\u6765\u6a21\u62df\u8fd9\u4e00\u8fc7\u7a0b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<p>from scipy.integrate import odeint<\/p>\n<h2><strong>\u5b9a\u4e49\u7b80\u5355\u8c10\u632f\u5b50\u7684\u5fae\u5206\u65b9\u7a0b<\/strong><\/h2>\n<p>def sho(y, t, k, m):<\/p>\n<p>    x, v = y<\/p>\n<p>    dydt = [v, -k\/m * x]<\/p>\n<p>    return dydt<\/p>\n<h2><strong>\u521d\u59cb\u6761\u4ef6<\/strong><\/h2>\n<p>x0 = 1.0  # \u521d\u59cb\u4f4d\u79fb<\/p>\n<p>v0 = 0.0  # \u521d\u59cb\u901f\u5ea6<\/p>\n<p>y0 = [x0, v0]<\/p>\n<h2><strong>\u5b9a\u4e49\u5f39\u6027\u7cfb\u6570\u548c\u8d28\u91cf<\/strong><\/h2>\n<p>k = 1.0<\/p>\n<p>m = 1.0<\/p>\n<h2><strong>\u5b9a\u4e49\u65f6\u95f4\u6570\u7ec4<\/strong><\/h2>\n<p>t = np.linspace(0, 10, 100)<\/p>\n<h2><strong>\u4f7f\u7528odeint\u51fd\u6570\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b<\/strong><\/h2>\n<p>sol = odeint(sho, y0, t, args=(k, m))<\/p>\n<h2><strong>\u7ed8\u5236\u4f4d\u79fb-\u65f6\u95f4\u56fe<\/strong><\/h2>\n<p>plt.plot(t, sol[:, 0])<\/p>\n<p>plt.xlabel(&#39;Time (s)&#39;)<\/p>\n<p>plt.ylabel(&#39;Displacement (m)&#39;)<\/p>\n<p>plt.title(&#39;Simple Harmonic Oscillator&#39;)<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u7b80\u5355\u8c10\u632f\u5b50\u7684\u5fae\u5206\u65b9\u7a0b\uff0c\u5e76\u4f7f\u7528SciPy\u7684<code>odeint<\/code>\u51fd\u6570\u6c42\u89e3\u8be5\u5fae\u5206\u65b9\u7a0b\u3002\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528Matplotlib\u5e93\u7ed8\u5236\u4e86\u4f4d\u79fb-\u65f6\u95f4\u56fe\u3002<\/p>\n<\/p>\n<p><h3>\u4e94\u3001MATPLOTLIB\u5e93\u7684\u53ef\u89c6\u5316<\/h3>\n<\/p>\n<p><p>Matplotlib\u662f\u4e00\u4e2a\u5f3a\u5927\u7684Python\u7ed8\u56fe\u5e93\uff0c\u7528\u4e8e\u521b\u5efa\u9759\u6001\u3001\u52a8\u753b\u548c\u4ea4\u4e92\u5f0f\u53ef\u89c6\u5316\u3002\u5b83\u4e0eNumPy\u548cSciPy\u65e0\u7f1d\u96c6\u6210\uff0c\u975e\u5e38\u9002\u5408\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97\u548c\u7269\u7406\u4eff\u771f\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u5b89\u88c5Matplotlib<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86Matplotlib\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">pip install matplotlib<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001Matplotlib\u5728\u7269\u7406\u4eff\u771f\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n<p><p>Matplotlib\u63d0\u4f9b\u4e86\u8bb8\u591a\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u521b\u5efa\u5404\u79cd\u7c7b\u578b\u7684\u56fe\u8868\u548c\u53ef\u89c6\u5316\u3002\u6211\u4eec\u5df2\u7ecf\u5728\u524d\u9762\u7684\u793a\u4f8b\u4e2d\u4f7f\u7528\u4e86Matplotlib\u6765\u7ed8\u5236\u4f4d\u79fb-\u65f6\u95f4\u56fe\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528Matplotlib\u521b\u5efa\u52a8\u753b\u3002<\/p>\n<\/p>\n<p><h3>\u516d\u3001\u521b\u5efa\u52a8\u753b<\/h3>\n<\/p>\n<p><p>\u52a8\u753b\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u76f4\u89c2\u5730\u7406\u89e3\u7269\u7406\u73b0\u8c61\u3002Matplotlib\u63d0\u4f9b\u4e86\u4e00\u4e2a<code>animation<\/code>\u5b50\u6a21\u5757\uff0c\u53ef\u4ee5\u7528\u4e8e\u521b\u5efa\u52a8\u753b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<p>from matplotlib.animation import FuncAnimation<\/p>\n<h2><strong>\u5b9a\u4e49\u65f6\u95f4\u6570\u7ec4<\/strong><\/h2>\n<p>t = np.linspace(0, 10, 1000)<\/p>\n<h2><strong>\u5b9a\u4e49\u4f4d\u79fb\u51fd\u6570\uff08\u7b80\u5355\u8c10\u632f\u5b50\uff09<\/strong><\/h2>\n<p>x = np.sin(t)<\/p>\n<h2><strong>\u521b\u5efa\u56fe\u5f62\u548c\u8f74<\/strong><\/h2>\n<p>fig, ax = plt.subplots()<\/p>\n<p>line, = ax.plot(t, x)<\/p>\n<h2><strong>\u521d\u59cb\u5316\u51fd\u6570<\/strong><\/h2>\n<p>def init():<\/p>\n<p>    line.set_ydata([np.nan] * len(t))<\/p>\n<p>    return line,<\/p>\n<h2><strong>\u66f4\u65b0\u51fd\u6570<\/strong><\/h2>\n<p>def update(frame):<\/p>\n<p>    line.set_ydata(np.sin(t - 0.1 * frame))<\/p>\n<p>    return line,<\/p>\n<h2><strong>\u521b\u5efa\u52a8\u753b<\/strong><\/h2>\n<p>ani = FuncAnimation(fig, update, frames=range(100), init_func=init, blit=True)<\/p>\n<h2><strong>\u663e\u793a\u52a8\u753b<\/strong><\/h2>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u521b\u5efa\u4e86\u4e00\u4e2a\u7b80\u5355\u8c10\u632f\u5b50\u7684\u52a8\u753b\u3002\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2a\u4f4d\u79fb\u51fd\u6570\uff0c\u5e76\u4f7f\u7528<code>FuncAnimation<\/code>\u51fd\u6570\u521b\u5efa\u52a8\u753b\u3002<code>init<\/code>\u51fd\u6570\u7528\u4e8e\u521d\u59cb\u5316\u52a8\u753b\uff0c<code>update<\/code>\u51fd\u6570\u7528\u4e8e\u66f4\u65b0\u52a8\u753b\u3002<\/p>\n<\/p>\n<p><h3>\u4e03\u3001SYMPY\u5e93\u7684\u7b26\u53f7\u8ba1\u7b97<\/h3>\n<\/p>\n<p><p>SymPy\u662f\u4e00\u4e2aPython\u5e93\uff0c\u7528\u4e8e\u7b26\u53f7\u6570\u5b66\u8ba1\u7b97\u3002\u5b83\u53ef\u4ee5\u7528\u4e8e\u4ee3\u6570\u3001\u5fae\u79ef\u5206\u3001\u79bb\u6563\u6570\u5b66\u7b49\u9886\u57df\u7684\u7b26\u53f7\u8fd0\u7b97\u3002SymPy\u975e\u5e38\u9002\u5408\u7528\u4e8e\u7269\u7406\u4eff\u771f\u4e2d\u7684\u7b26\u53f7\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u5b89\u88c5SymPy<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86SymPy\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">pip install sympy<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001SymPy\u5728\u7269\u7406\u4eff\u771f\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n<p><p>SymPy\u63d0\u4f9b\u4e86\u8bb8\u591a\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528SymPy\u8fdb\u884c\u7b26\u53f7\u5fae\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><h3>\u516b\u3001\u7b26\u53f7\u5fae\u79ef\u5206<\/h3>\n<\/p>\n<p><p>\u7b26\u53f7\u5fae\u79ef\u5206\u662f\u7269\u7406\u4eff\u771f\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u5de5\u5177\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528SymPy\u6765\u8fdb\u884c\u7b26\u53f7\u5fae\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import sympy as sp<\/p>\n<h2><strong>\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/strong><\/h2>\n<p>t = sp.symbols(&#39;t&#39;)<\/p>\n<p>x = sp.Function(&#39;x&#39;)(t)<\/p>\n<h2><strong>\u5b9a\u4e49\u7b80\u5355\u8c10\u632f\u5b50\u7684\u5fae\u5206\u65b9\u7a0b<\/strong><\/h2>\n<p>diff_eq = sp.Eq(x.diff(t, t) + x, 0)<\/p>\n<h2><strong>\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b<\/strong><\/h2>\n<p>solution = sp.dsolve(diff_eq)<\/p>\n<p>print(solution)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528SymPy\u5b9a\u4e49\u4e86\u7b80\u5355\u8c10\u632f\u5b50\u7684\u5fae\u5206\u65b9\u7a0b\uff0c\u5e76\u6c42\u89e3\u4e86\u8be5\u5fae\u5206\u65b9\u7a0b\u3002<\/p>\n<\/p>\n<p><h3>\u4e5d\u3001PYBULLET\u5e93\u7684\u7269\u7406\u5f15\u64ce<\/h3>\n<\/p>\n<p><p>PyBullet\u662f\u4e00\u4e2a\u7528\u4e8e\u7269\u7406\u4eff\u771f\u548c\u673a\u5668\u4eba\u63a7\u5236\u7684\u5f00\u6e90\u5e93\u3002\u5b83\u63d0\u4f9b\u4e86\u4e00\u4e2a\u9ad8\u6548\u7684\u7269\u7406\u5f15\u64ce\uff0c\u53ef\u4ee5\u7528\u4e8e\u6a21\u62df\u521a\u4f53\u52a8\u529b\u5b66\u3001\u67d4\u4f53\u52a8\u529b\u5b66\u3001\u78b0\u649e\u68c0\u6d4b\u7b49\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u5b89\u88c5PyBullet<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86PyBullet\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">pip install pybullet<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001PyBullet\u5728\u7269\u7406\u4eff\u771f\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n<p><p>PyBullet\u63d0\u4f9b\u4e86\u8bb8\u591a\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u7269\u7406\u4eff\u771f\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528PyBullet\u8fdb\u884c\u7b80\u5355\u7684\u521a\u4f53\u52a8\u529b\u5b66\u4eff\u771f\u3002<\/p>\n<\/p>\n<p><h3>\u5341\u3001\u521a\u4f53\u52a8\u529b\u5b66\u4eff\u771f<\/h3>\n<\/p>\n<p><p>\u521a\u4f53\u52a8\u529b\u5b66\u662f\u7269\u7406\u4eff\u771f\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u9886\u57df\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528PyBullet\u6765\u6a21\u62df\u521a\u4f53\u52a8\u529b\u5b66\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import pybullet as p<\/p>\n<p>import time<\/p>\n<h2><strong>\u8fde\u63a5\u5230\u7269\u7406\u5f15\u64ce<\/strong><\/h2>\n<p>p.connect(p.GUI)<\/p>\n<h2><strong>\u52a0\u8f7d\u5e73\u9762\u548c\u4e00\u4e2a\u7acb\u65b9\u4f53<\/strong><\/h2>\n<p>plane_id = p.loadURDF(&quot;plane.urdf&quot;)<\/p>\n<p>cube_id = p.loadURDF(&quot;r2d2.urdf&quot;, [0, 0, 1])<\/p>\n<h2><strong>\u8fd0\u884c\u4eff\u771f<\/strong><\/h2>\n<p>for _ in range(10000):<\/p>\n<p>    p.stepSimulation()<\/p>\n<p>    time.sleep(1.\/240.)<\/p>\n<h2><strong>\u65ad\u5f00\u8fde\u63a5<\/strong><\/h2>\n<p>p.disconnect()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528PyBullet\u8fde\u63a5\u5230\u7269\u7406\u5f15\u64ce\uff0c\u52a0\u8f7d\u4e86\u4e00\u4e2a\u5e73\u9762\u548c\u4e00\u4e2a\u7acb\u65b9\u4f53\uff0c\u5e76\u8fd0\u884c\u4e86\u4eff\u771f\u3002<\/p>\n<\/p>\n<p><h3>\u5341\u4e00\u3001PYGAME\u5e93\u7684\u6e38\u620f\u5f00\u53d1<\/h3>\n<\/p>\n<p><p>Pygame\u662f\u4e00\u4e2a\u7528\u4e8e\u5f00\u53d12D\u6e38\u620f\u7684\u5f00\u6e90\u5e93\u3002\u5b83\u63d0\u4f9b\u4e86\u8bb8\u591a\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u5904\u7406\u56fe\u5f62\u3001\u58f0\u97f3\u3001\u4e8b\u4ef6\u7b49\u3002Pygame\u975e\u5e38\u9002\u5408\u7528\u4e8e\u7269\u7406\u4eff\u771f\u4e2d\u7684\u4ea4\u4e92\u5f0f\u53ef\u89c6\u5316\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u5b89\u88c5Pygame<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86Pygame\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">pip install pygame<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001Pygame\u5728\u7269\u7406\u4eff\u771f\u4e2d\u7684\u5e94\u7528<\/h4>\n<\/p>\n<p><p>Pygame\u63d0\u4f9b\u4e86\u8bb8\u591a\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u521b\u5efa\u4ea4\u4e92\u5f0f\u53ef\u89c6\u5316\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528Pygame\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u7269\u7406\u4eff\u771f\u3002<\/p>\n<\/p>\n<p><h3>\u5341\u4e8c\u3001\u521b\u5efa\u7b80\u5355\u7684\u7269\u7406\u4eff\u771f<\/h3>\n<\/p>\n<p><p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528Pygame\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u7269\u7406\u4eff\u771f\uff0c\u4f8b\u5982\u4e00\u4e2a\u5f39\u8df3\u7403\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import pygame<\/p>\n<p>import sys<\/p>\n<h2><strong>\u521d\u59cb\u5316Pygame<\/strong><\/h2>\n<p>pygame.init()<\/p>\n<h2><strong>\u8bbe\u7f6e\u5c4f\u5e55\u5c3a\u5bf8<\/strong><\/h2>\n<p>screen = pygame.display.set_mode((800, 600))<\/p>\n<h2><strong>\u5b9a\u4e49\u989c\u8272<\/strong><\/h2>\n<p>WHITE = (255, 255, 255)<\/p>\n<p>RED = (255, 0, 0)<\/p>\n<h2><strong>\u5b9a\u4e49\u7403\u7684\u5c5e\u6027<\/strong><\/h2>\n<p>ball_pos = [400, 300]<\/p>\n<p>ball_vel = [2, 2]<\/p>\n<p>ball_radius = 20<\/p>\n<h2><strong>\u8fd0\u884c\u6e38\u620f\u5faa\u73af<\/strong><\/h2>\n<p>while True:<\/p>\n<p>    for event in pygame.event.get():<\/p>\n<p>        if event.type == pygame.QUIT:<\/p>\n<p>            pygame.quit()<\/p>\n<p>            sys.exit()<\/p>\n<p>    # \u66f4\u65b0\u7403\u7684\u4f4d\u7f6e<\/p>\n<p>    ball_pos[0] += ball_vel[0]<\/p>\n<p>    ball_pos[1] += ball_vel[1]<\/p>\n<p>    # \u78b0\u649e\u68c0\u6d4b<\/p>\n<p>    if ball_pos[0] &lt;= ball_radius or ball_pos[0] &gt;= 800 - ball_radius:<\/p>\n<p>        ball_vel[0] = -ball_vel[0]<\/p>\n<p>    if ball_pos[1] &lt;= ball_radius or ball_pos[1] &gt;= 600 - ball_radius:<\/p>\n<p>        ball_vel[1] = -ball_vel[1]<\/p>\n<p>    # \u6e05\u5c4f<\/p>\n<p>    screen.fill(WHITE)<\/p>\n<p>    # \u7ed8\u5236\u7403<\/p>\n<p>    pygame.draw.circle(screen, RED, ball_pos, ball_radius)<\/p>\n<p>    # \u66f4\u65b0\u663e\u793a<\/p>\n<p>    pygame.display.flip()<\/p>\n<p>    # \u63a7\u5236\u5e27\u7387<\/p>\n<p>    pygame.time.Clock().tick(60)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Pygame\u521b\u5efa\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u7269\u7406\u4eff\u771f\uff0c\u6a21\u62df\u4e86\u4e00\u4e2a\u5f39\u8df3\u7403\u3002\u6211\u4eec\u5b9a\u4e49\u4e86\u7403\u7684\u5c5e\u6027\uff0c\u5e76\u5728\u6e38\u620f\u5faa\u73af\u4e2d\u66f4\u65b0\u7403\u7684\u4f4d\u7f6e\u548c\u8fdb\u884c\u78b0\u649e\u68c0\u6d4b\u3002\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528Pygame\u7684\u7ed8\u56fe\u51fd\u6570\u7ed8\u5236\u7403\u5e76\u66f4\u65b0\u663e\u793a\u3002<\/p>\n<\/p>\n<p><h3>\u5341\u4e09\u3001\u603b\u7ed3<\/h3>\n<\/p>\n<p><p>\u4f7f\u7528Python\u8fdb\u884c\u7269\u7406\u4eff\u771f\u9700\u8981\u7ed3\u5408\u4f7f\u7528\u591a\u4e2a\u5e93\uff0c\u5982NumPy\u3001SciPy\u3001Matplotlib\u3001SymPy\u3001PyBullet\u548cPygame\u7b49\u3002\u8fd9\u4e9b\u5e93\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u7528\u4e8e\u8fdb\u884c\u79d1\u5b66\u8ba1\u7b97\u3001\u7b26\u53f7\u8fd0\u7b97\u3001\u7269\u7406\u5f15\u64ce\u4eff\u771f\u548c\u4ea4\u4e92\u5f0f\u53ef\u89c6\u5316\u3002\u901a\u8fc7\u5408\u7406\u5229\u7528\u8fd9\u4e9b\u5de5\u5177\uff0c\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u590d\u6742\u7684\u7269\u7406\u4eff\u771f\uff0c\u5e76\u8fdb\u884c\u6df1\u5165\u7684\u7814\u7a76\u548c\u5206\u6790\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u9009\u62e9\u9002\u5408\u7684\u7269\u7406\u5f15\u64ce\u8fdb\u884cPython\u7269\u7406\u4eff\u771f\uff1f<\/strong><br \/>\u5728\u8fdb\u884c\u7269\u7406\u4eff\u771f\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u7269\u7406\u5f15\u64ce\u81f3\u5173\u91cd\u8981\u3002\u5e38\u7528\u7684Python\u7269\u7406\u5f15\u64ce\u6709PyBullet\u3001Pygame\u3001Panda3D\u7b49\u3002PyBullet\u9002\u5408\u4e8e\u673a\u5668\u4eba\u548c\u521a\u4f53\u52a8\u529b\u5b66\u6a21\u62df\uff0cPygame\u5219\u9002\u54082D\u6e38\u620f\u5f00\u53d1\uff0cPanda3D\u66f4\u9002\u54083D\u56fe\u5f62\u548c\u6e38\u620f\u5f00\u53d1\u3002\u6839\u636e\u4f60\u7684\u9879\u76ee\u9700\u6c42\u3001\u4eff\u771f\u590d\u6742\u5ea6\u548c\u76ee\u6807\u5e73\u53f0\uff0c\u6311\u9009\u6700\u5408\u9002\u7684\u5f15\u64ce\u53ef\u4ee5\u63d0\u9ad8\u4eff\u771f\u6548\u679c\u548c\u5f00\u53d1\u6548\u7387\u3002<\/p>\n<p><strong>\u5982\u4f55\u5728Python\u4e2d\u5b9e\u73b0\u7b80\u5355\u7684\u7269\u7406\u4eff\u771f\uff1f<\/strong><br \/>\u5b9e\u73b0\u7b80\u5355\u7684\u7269\u7406\u4eff\u771f\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528NumPy\u5e93\u8fdb\u884c\u6570\u503c\u8ba1\u7b97\u3002\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u5b9a\u4e49\u7269\u4f53\u7684\u8d28\u91cf\u3001\u4f4d\u7f6e\u3001\u901f\u5ea6\u548c\u52a0\u901f\u5ea6\u7b49\u57fa\u672c\u7269\u7406\u5c5e\u6027\u3002\u901a\u8fc7\u4e0d\u65ad\u8fed\u4ee3\u66f4\u65b0\u8fd9\u4e9b\u5c5e\u6027\uff0c\u53ef\u4ee5\u6a21\u62df\u7269\u4f53\u5728\u91cd\u529b\u3001\u6469\u64e6\u529b\u7b49\u4f5c\u7528\u4e0b\u7684\u8fd0\u52a8\u3002\u4f7f\u7528matplotlib\u7b49\u53ef\u89c6\u5316\u5e93\uff0c\u53ef\u4ee5\u5c06\u8fd0\u52a8\u8f68\u8ff9\u7ed8\u5236\u51fa\u6765\uff0c\u4ece\u800c\u76f4\u89c2\u5c55\u793a\u4eff\u771f\u7ed3\u679c\u3002<\/p>\n<p><strong>\u6709\u4ec0\u4e48\u5f00\u6e90\u9879\u76ee\u53ef\u4ee5\u5e2e\u52a9\u6211\u5b66\u4e60Python\u7269\u7406\u4eff\u771f\uff1f<\/strong><br \/>\u8bb8\u591a\u5f00\u6e90\u9879\u76ee\u80fd\u591f\u5e2e\u52a9\u4f60\u6df1\u5165\u7406\u89e3Python\u7269\u7406\u4eff\u771f\u3002\u6bd4\u5982\uff0cBox2D\u662f\u4e00\u4e2a2D\u7269\u7406\u5f15\u64ce\uff0c\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u793a\u4f8b\u4ee3\u7801\u548c\u6587\u6863\uff0c\u9002\u5408\u521d\u5b66\u8005\u5b66\u4e60\u3002\u53e6\u4e00\u4e2a\u4f8b\u5b50\u662fPyBullet\uff0c\u5b83\u4e0d\u4ec5\u9002\u5408\u7269\u7406\u4eff\u771f\uff0c\u8fd8\u63d0\u4f9b\u4e86<a href=\"https:\/\/docs.pingcode.com\/ask\/59192.html\" target=\"_blank\">\u673a\u5668\u5b66\u4e60<\/a>\u7684\u63a5\u53e3\uff0c\u9002\u5408\u6709\u4e00\u5b9a\u57fa\u7840\u7684\u5f00\u53d1\u8005\u3002GitHub\u4e0a\u6709\u8bb8\u591a\u4e0e\u7269\u7406\u4eff\u771f\u76f8\u5173\u7684\u9879\u76ee\uff0c\u4f60\u53ef\u4ee5\u901a\u8fc7\u67e5\u627e\u8fd9\u4e9b\u8d44\u6e90\u6765\u83b7\u53d6\u7075\u611f\u548c\u5b66\u4e60\u7ecf\u9a8c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u4f7f\u7528Python\u8fdb\u884c\u7269\u7406\u4eff\u771f\u7684\u6838\u5fc3\u5728\u4e8e\u7075\u6d3b\u8fd0\u7528\u79d1\u5b66\u8ba1\u7b97\u5e93\u3001\u6570\u503c\u65b9\u6cd5\u3001\u4ee5\u53ca\u7269\u7406\u5b66\u57fa\u672c\u539f\u7406\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u5e38\u7528\u7684\u65b9\u6cd5\u548c [&hellip;]","protected":false},"author":3,"featured_media":1173904,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1173895"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1173895"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1173895\/revisions"}],"predecessor-version":[{"id":1173905,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1173895\/revisions\/1173905"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1173904"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1173895"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1173895"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1173895"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}