Exponential map in the generalized Dido problem

Yu. L. Sachkov

Sbornik. Mathematics, Tome 194 (2003) no. 9, pp. 1331-1359

Résumé

The generalized Dido problem is stated as an optimal control problem in 5-dimensional space with 2-dimensional control and quadratic cost functional, which is a nilpotent sub-Riemannian problem with the growth vector (2, 3, 5). Extremals of this problem are parametrized by Jacobian elliptic functions.

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