Defining single-particle phase spaces in a system of interacting particles is problematic, as fixing the states of other particles reduces the system to a trivial one-particle scenario. An alternative approach involves creating a phase sub-space using weighted averages of multiple particles' coordinates. Linear algebra can facilitate various representations of particle interactions. In some cases, approximations can be made where certain degrees of freedom are treated as independent, such as in systems with a heavy harmonic oscillator coupled to lighter oscillators. Overall, the complexity of interactions complicates the establishment of single-particle phase spaces.