The “Falling Cat” Problem and Riemannian Geometry of Shape Space: An Application to the Structural Transition Dynamics of Molecules

Abstract

The so-called “falling cat” problem, which is concerned with the coupling between internal motions and rotations of a flexible body, is introduced. I give a geometric interpretation of the Eckart condition, which is frequently used for the approximate separation of rotations and internal motions of polyatomic molecules. It is shown that the separation procedure based on the Eckart condition disregards the intrinsically “curved” nature of molecular internal space (shape space). The “curved” nature of shape space is shown to have considerable effects on structural transition dynamics of polyatomic molecules.