Rigid rotor

The rigid rotor is a mechanical model that is used to explain rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space three angles known as Euler angles are required. A special rigid rotor is the linear rotor which requires only two angles to describe its orientation. An example of a linear rotor is a diatomic molecule. More general molecules like water (asymmetric rotor), ammonia (symmetric rotor), or methane (spherical rotor) are 3-dimensional, see classification of molecules.

The linear rigid rotor model consists of two point masses located at fixed distances from their center of mass. The fixed distance between the two masses and the values of the masses are the only characteristics of the rigid model. However, for many actual diatomics this model is too restrictive since distances are usually not completely fixed. Corrections on the rigid model can be made to compensate for small variations in the distance. Even in such a case the rigid rotor model is a useful point of departure (zeroth-order model).

The classical linear rotor consists of two point masses ${\displaystyle m_{1}}$ and ${\displaystyle m_{2}}$ (with reduced mass ${\displaystyle \mu ={\frac {m_{1}m_{2}}{m_{1}+m_{2}}}}$) each at a distance ${\displaystyle R}$. The rotor is rigid if ${\displaystyle R}$ is independent of time. The kinematics of a linear rigid rotor is usually described by means of spherical polar coordinates, which form a coordinate system of R³. In the physics convention the coordinates are the co-latitude (zenith) angle ${\displaystyle \theta \,}$, the longitudinal (azimuth) angle ${\displaystyle \varphi \,}$ and the distance ${\displaystyle R}$. The angles specify the orientation of the rotor in space. The kinetic energy ${\displaystyle T}$ of the linear rigid rotor is given by

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