关于振动与转动

 1. 简正模式

Normal Modes

Normal modes are used to describe the different vibrational motions in molecules. Each mode can be characterized by a different type of motion and each mode has a certain symmetry associated with it. Group theory is a useful tool in order to determine what symmetries the normal modes contain and predict if these modes are IR and/or Raman active. Consequently, IR and Raman spectroscopy is often used for vibrational spectra.

Overview of Normal Modes

In general, a normal mode is an independent motion of atoms in a molecule that occurs without causing movement to any of the other modes. Normal modes, as implied by their name, are orthogonal to each other. In order to discuss the quantum-mechanical equations that govern molecular vibrations it is convenient to convert Cartesian coordinates into so called normal coordinates. Vibrations in polyatomic molecules are represented by these normal coordinates.

The normal modes of vibration are: asymmetric, symmetric, wagging, twisting, scissoring, and rocking for polyatomic molecules.

Symmetric Stretching	Asymmetric Stretching	Wagging
Twisting	Scissoring	Rocking

Figure 1

: Six types of Vibrational Modes. Images used with permission (Public Domain; Tiago Becerra Paolini).

2. 关于转动自由度

自由度指物体能够对坐标系进行独立运动的数目，物体所能进行的运动如下图：

一个物体可以相对于坐标系，进行三个平移和三个旋转运动，即一个简单的物体有六个自由度。

运动副是两构件直接接触并能产生相对运动的活动联接。运动副引入约束进而限制6个自由度中的某些自由度。在机器人学中，运动副也成为机器人的关节。

上图中列举了一些简单的运动副，按由上及下，由左及右的顺序依次为移动副、转动副、螺旋副、凸轮和球铰。移动副限制了一个方向移动的所有自由度，因而它只剩下一个自由度；转动副限制了一个方向转动以外的所有自由度，它也只剩下一个自由度；最后一个球铰引入3个约束，限制了所有方向的移动，因而只具有x、y和z轴方向的转动，即3个自由度。

https://www.sohu.com/a/114524288_489960