The Non-Principal-Axis Rotation and Convex Shape Model of Earth Quasi-Satellite and the Target of China's Tianwen-2 Mission (469219) Kamo`oalewa

(469219) Kamooalewa is the most stable Earth quasi-satellite and the target of China's Tianwen-2 asteroid sample return mission. Due to its small size, fast rotation, and the limited observing geometry accessible from the ground, many physical properties of Kamooalewa remain poorly constrained, including the rotational state and shape. We obtained three epochs of high-cadence, high signal-to-noise photometric lightcurves of Kamooalewa with the Gemini North Telescope from 2026 April to May, supplemented by one lightcurve from the Lowell Discovery Telescope in 2026 May. Our analysis suggests that Kamooalewa is in a non-principal-axis rotation with an elongated shape. Four possible solutions exist, including a long-axis mode (LAM) solution and a short-axis mode (SAM) solution, as well as their corresponding mirrored angular momentum directions. The most preferable solution has a LAM model with a precession period $P_{\varphi }=27.65\pm 0.03\text{ min}$ and a rotational period $P_{\psi }=50.49\pm 0.08\text{ min}$, and the angular momentum points to ecliptic coordinates $(\lambda ,\beta )=({226}^{\mathrm{o}}\pm {20}^{\mathrm{o}},-{39}^{\mathrm{o}}\pm 20\mathrm{o})$, although we cannot rule out other solutions or other close-by periods due to aliasing. We also derived a convex shape inversion for the LAM models with consistent rotational parameters but could not find a satisfactory inversion for the SAM models. The corresponding angular momentum points to $(\lambda ,\beta )=({225}^{\mathrm{o}},-{43}^{\mathrm{o}})$, and the periods are $P_{\varphi }=27.90\text{ min}$ and $P_{\psi }=49.66\text{ min}$. The non-principal-axis rotation provides additional constraints on the dynamic history or the internal structure of Kamo`oalewa.