In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three angles, known as Euler angles (ψ, θ, φ). A special rigid rotor is the linear rotor requiring only two angles to describe, for example a diatomic molecule such as HI, HCl, CO. More general molecules are 3-dimensional, such as water (asymmetric rotor), ammonia (symmetric rotor), or methane (spherical rotor).
Linear rotor 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 diatomic molecules this model is too restrictive since distances are usually not 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).
Classical linear rigid rotor The classical linear rotor consists of two point masses m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} (with reduced mass μ = m 1 m 2 m 1 + m 2 {\textstyle \mu ={\frac {m_{1}m_{2}}{m_{1}+m_{2}}}} ) at a distance R {\displaystyle R} of each other. The rotor is rigid if R {\displaystyle R} is independent of time. The kinematics of a linear rigid rotor is usually described by means of spherical polar coordinates ( θ , φ , R {\displaystyle \theta ,\varphi ,R} ), which form a coordinate system of R3. In the physics convention the coordinates are the co-latitude (zenith) angle θ {\displaystyle \theta \,} , the longitudinal (azimuth) angle φ {\displaystyle \varphi \,} and the distance R {\displaystyle R} . The angles specify the orientation of the rotor in space. The kinetic energy T {\displaystyle T} of the linear rigid rotor is given by
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