### Periodic solutions of the perturbed symmetric Euler top

#### Abstract

We study the problem of persistence of $T$-periodic solutions of

the celebrated symmetric Euler top when subjected to a small

$T$-periodic stimulus. All solutions of the unperturbed system are

periodic (of different periods, including continua of equilibria).

In the case that the perturbation depends also on the three

components of the angular momentum (the unknowns of the system) we

provide bifurcation functions whose simple zeros correspond to

$T$-periodic solutions of the perturbed system.

the celebrated symmetric Euler top when subjected to a small

$T$-periodic stimulus. All solutions of the unperturbed system are

periodic (of different periods, including continua of equilibria).

In the case that the perturbation depends also on the three

components of the angular momentum (the unknowns of the system) we

provide bifurcation functions whose simple zeros correspond to

$T$-periodic solutions of the perturbed system.

#### Keywords

Euler top; periodic perturbation; periodic solutions; bifurcation function

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