Almost periodic light curves of small rotating bodies

The rotation of a rigid body can be expressed by evolution equations for classical Euler angles. For torque-free evolution, analytic solutions for two Euler angle periods are available.
In the presence of a torque generating force, such as in sublimation processes, a perturbative treatment is sometimes possible [1,2]. The body will never return to its initial state, unless the rotation around the body fixed angular momentum after one revolution is commensurable with 2π.
Therefore, light-curves of an irregularly shaped object are in general never repeating exactly.
However, the Fourier spectrum of this object still shows sharp and distinct peaks in various combinations of averaged periods derived from Euler angles [3,4]. We relate this finding to the theory of almost periodic functions and discuss specific examples of light curves for non-principal axis rotators.

[1] Kramer et al. 2019, A&A 630, A3, doi:10.1051/0004-6361/201834349
[2] Läuter&Kramer 2025, A&A 699, A75, doi:10.1051/0004-6361/202553845
[3] Kaasalainen, 2001, A&A 376, 302–309, doi:10.1051/0004-6361:20010935
[4] Samarasinha et al. 2011, ApJL 734, L3, doi:10.1088/2041-8205/734/1/L3