Maxwell strata in sub-Riemannian problem on the group of motions of a   plane
  The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parametrized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained. 
I. Moiseev, Yu. L. Sachkov