欧氏空间和non-Euclidean geometry空间框架的静力学和运动学
Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry
摘要：
这是一篇关于欧几里得、双曲和球面几何中框架的无穷小刚性的综述文章。我们讨论的等价性的静态和运动学配方的无穷小刚度，静力学的投影解释（代表力作为bivectors），和无穷小Pogorelov地图，建立对应关系的无穷小运动的框架和它的测地线图像。此外，我们描述的麦克斯韦-克雷莫纳之间的对应平衡负载和多面体升降机，无论是欧几里德和非欧几里德框架。
英文摘要：
This is a survey article on the infinitesimal rigidity of frameworks in Euclidean, hyperbolic, and spherical geometry. We discuss the equivalence of the static and kinematic formulations of the infinitesimal rigidity, the projective interpretation of statics (representing forces as bivectors), and the infinitesimal Pogorelov maps that establish correspondence between infinitesimal motions of a framework and of its geodesic image. Also we describe the Maxwell-Cremona correspondence between equilibrium loads and polyhedral lifts, both for Euclidean and for non-Euclidean frameworks.
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