= Rigid rotor
{wiki}
A <rigid rotor> models rotational motion with fixed internal separations. Its use in the synthetic <Stark effect> figure omits vibrational motion and additional interactions in real <molecules>.
Rigidity fixes the <molecular geometry>, not the orientation, and does not require a spherical mass distribution. Remove motion of the <centre of mass>, choose <principal axes> of the <inertia tensor>, and write the classical <rotational kinetic energy> as
$$
T_{\rm rot}=\frac12\left(I_a\omega_a^2+I_b\omega_b^2+I_c\omega_c^2\right)
=\frac{L_a^2}{2I_a}+\frac{L_b^2}{2I_b}+\frac{L_c^2}{2I_c}.
$$
Here $I_a,I_b,I_c$ are the principal <moments of inertia>, $\omega_a,\omega_b,\omega_c$ components of <angular velocity>, and $L_a,L_b,L_c$ components of <angular momentum>. Quantization replaces these last components by <angular momentum operators>. Different principal <moments of inertia> produce different spectra: the single-constant <linear rigid rotor> is a special case, not a formula for every <molecule>.<Lecture 24 Supplement: Energy levels of a Rigid Rotor by Dudley Herschbach>[printed p. 1: principal-axis energy and classification; pp. 4–5: asymmetric rotors]{ref}
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