V2EX principal axis

Principal Axis

释义 Definition(中文)

principal axis主轴 / 主轴线。指在数学、物理或工程中最重要的轴线方向,常见于:

  • 几何与解析几何:圆锥曲线(如椭圆)的长轴/短轴等“主轴”;
  • 线性代数:二次型或协方差矩阵对角化后对应的主方向(主轴)
  • 力学:刚体的主惯性轴(principal axes of inertia),即使惯性矩阵对角化的轴系。
    (不同学科含义略有侧重,但核心都是“最主要、最能代表结构或变化方向的轴”。)

发音 Pronunciation (IPA)

/prnspl kss/

例句 Examples

The ellipse’s principal axis is horizontal.
这个椭圆的主轴是水平的。

By rotating the coordinate system to align with the principal axis, we can simplify the equation and interpret the data more clearly.
通过旋转坐标系使其与主轴对齐,我们可以简化方程,并更清晰地解释数据。

词源 Etymology(中文)

principal 来自拉丁语 prnceps(“第一的、首要的”),含“最重要的”之意;axis 来自拉丁语 axis(“轴、车轴”)。合起来 principal axis 字面意思是“首要的轴”,在科学语境中引申为“描述形状、分布或转动特性时最关键的轴线/方向”。

相关词 Related Words

文学与经典作品 Literary Mentions(作品示例)

  • The Feynman Lectures on Physics(费曼《物理学讲义》)
  • Classical Mechanics(Herbert Goldstein,《经典力学》)
  • Introduction to Linear Algebra(Gilbert Strang,《线性代数导论》)
  • Linear Algebra Done Right(Sheldon Axler,《线性代数应该这样学》)
  • Numerical Recipes(《数值算法》系列书)
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