Reduced Liouville equation in generalized coordinates

Following the same procedures as in Sec. 3.3, we can also write reduced forms of the Liouville equation in generalized coordinates and conjugate momenta. Integrating Eq. (2.2) over (s-u) variables leads to 

Because of the possible complicated nature of the hamiltonian and associated variables, no further general simplification of Eq. (3.58) can be performed every particular system must be analyzed separately. This is illustrated in Example 3.2. 

Example 3.2 Reduced Liouviiie Equation for Interacting Dipole It is desired to write the lowest-order version of the contracted Liouviiie equation for a system of interacting dipoles. An important physical example of this is a polar gas composed of iV indistinguishable molecules, such as those listed in Table 1.2. 

From our previous examples, Eqs. (1.41) and (2.63) we can immediately write the hamiltonian for N interacting dipoles as 

Using the hamiltonian, Eq. (3.60), the second term on the left-hand side of Eq. (3.63) can be written as 

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See also in sourсe #XX -- [ , ]

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