The Free Euler Rigid Body Revisited

We review from a different perspective the approach and solution to torque-free Euler equations, also called free asymmetric top equations. aim simplify broaden study of rigid body. This is an old but important integrable problem that has two first integrals: energy angular momentum. reduce this by eliminating time as independent variable in three autonomous equations written cylindrical dimensionless variables, which allows geometric function angle ψ, means continuous deformations dependent on parameters κ e0. The parameter space divided into six disjoint regions, whose boundaries are separatices degenerated cases. solutions given terms trigonometric functions cylindric ψ.