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In the present paper, we obtain explicit formulae for geodesics in someleft-invariant sub-Finsler problems on Heisenberg groups $\mathbb{H}_{2n+1}$.Our main assumption is the following: the compact convex set of unit velocitiesat identity admits a generalization of spherical coordinates. This includesconvex hulls and sums of coordinate 2-dimensional sets, all left-invariantsub-Riemannian structures on $\mathbb{H}_{2n+1}$, and unit balls in$L_p$-metric for $1\le p\le\infty$. In the last case, extremals are obtained interms of incomplete Euler integral of the first kind.

Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry