This paper provides an expression of the spherical $p$-elastic curves (bottom of page 9) and claims that this expression is obtained by adapting the results of this paper which treats the case $p=2$. However I didn't find the expression of the spherical elastic curve $\gamma$ in the second paper. There's the so-called wavelength studied in the appendix but I didn't see it in the paper, hence my misunderstanding.
Would you know the expression of $\gamma$ for $p=2$? (similar to the one given in the first paper).