A Note on Geodesics on Ellipsoid

The purpose of this note is to show that the Jacobi problem of geodesics on ellipsoid [1], [2], [3] may be reduced to a more simple case, namely, to the Clebsch problem [4]. The last one is the problem with quadratic nonlinearity and may be solved directly by using of Weber's approach [5] in terms of multi-dimensional theta functions.