The rotational kinetic energy of a rotator with three degrees of freedom can be written as [
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The rotational kinetic energy of a rotator with three degrees of freedom can be written as
\[
\varepsilon_{\mathrm{rot}}=\frac{M_{\xi}^{2}}{2 I_{1}}+\frac{M_{\eta}^{2}}{2 I_{2}}+\frac{M_{\zeta}^{2}}{2 I_{3}}
\]
where \((\xi, \eta, \zeta)\) are coordinates in a rotating frame of reference whose axes coincide with the principal axes of the rotator, while \(\left(M_{\xi}, M_{\eta}, M_{\zeta}ight)\) are the corresponding angular momenta. Carrying out integrations in the phase space of the rotator, derive expression (6.5.41) for the partition function \(j_{\mathrm{rot}}(T)\) in the classical approximation.
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