论文标题
部分可观测时空混沌系统的无模型预测
Teaching Rotational Physics with Bivectors
论文作者
论文摘要
传统上将角动量教为（伪）矢量数量，与跨产品紧密相关。这种方法是专家熟悉的，但对学生来说具有挑战性，并且充满了微妙之处。在这里，我们提出了一种替代的教学方法：使用双分动物描述了角动量，可以将其可视化为面积和方向的“瓷砖”，其组分形成抗对称矩阵。尽管在历史上已经在时空分类或几何代数等专业环境中研究了双分动物，但它们比跨产品更复杂。 Bivector语言为旋转物理学提供了更基本的定义，并为了解相对性和额外维度的旋转打开了大门。
Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical approach: angular momentum is described using bivectors, which can be visualized as "tiles" with area and orientation and whose components form an antisymmetric matrix. Although bivectors have historically been studied in specialized contexts like spacetime classification or geometric algebra, they are no more complicated to understand than cross products. The bivector language provides a more fundamental definition for rotational physics, and opens the door to understanding rotations in relativity and in extra dimensions.
