Obtain the paths of the l-point for an unsymmetrical body

Question

Obtain the paths of the L-point for an unsymmetrical body, as shown in given Figure. These were obtained by solving Euler's equations, together with the equations numerically.

e₁^· = ω₃e₂ - ω₂e₃,

e₂^· = ω₁e₃ - ω₃e₁,

e₃^· = ω₂e₁ - ω₁e₂,

[Mathematica handled the solution of these twelve simultaneous equations with ease!]