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We show that the classical model of Euler top (freely rotating, generallyasymmetric rigid body), possibly supplemented with a rotor, corresponds to ageneralized Lipkin-Meshkov-Glick (LMG) model describing phenomena of variousbranches of quantum physics. Classical effects such as free precession of asymmetric top, Feynman's wobbling plate, tennis-racket instability and theDzhanibekov effect, attitude control of satellites by momentum wheels, ortwisting somersault dynamics, have their counterparts in quantum effects thatinclude spin squeezing by one-axis twisting and two-axis countertwisting,transitions between the Josephson and Rabi regimes of a Bose-Einsteincondensate in a double-well potential, and other quantum critical phenomena.The parallels enable us to expand the range of explored quantum phasetransitions in the generalized LMG model, as well as to present a classicalanalogy of the recently proposed LMG Floquet time crystal.

Euler top with a rotor: classical analogies of spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model