The slow motion of a self-gravitating CP 1 lump is investigated in the approximation of geodesic flow on the moduli space of unit degree static solutions M1. It is found that moduli which are frozen in the absence of gravity, parametrizing the lump’s width and internal orientation, may vary once gravitational effects are included. If gravitational coupling is sufficiently strong, the presence o...

In this paper we address the general problem of approximating, in a certain optimal way, non admissible motions of a kinematic system with nonholonomic constraints. Since this kind of problems falls into the general subriemannian geometric setting, it is natural to consider optimality in the sense of approximating by means of subriemannian geodesics. We consider systems modeled by a subriemanni...

We consider the problem Pcurve of minimizing ∫ ` 0 √ β 2 + |κ(s)|2ds for a planar curve having fixed initial and final positions and directions. Here κ is the curvature of the curve with free total length `. This problem comes from a 2D model of geometry of vision due to Petitot, Citti and Sarti. Here we will provide a general theory on cuspless sub-Riemannian geodesics within a sub-Riemannian ...

We present a general framework for the optimal control of driftless nonlinear systems defined by means of distributions of smooth vector fields that generate nilpotent Lie algebras. A smooth varying inner product on the planes of the distribution, yields the energy functional that allows to approach the optimal control problem as a sub-Riemannian geodesic problem. This class of systems is relev...

It is an important problem to compute the geodesics on a surface in many fields. To find the geodesics in practice, however, the traditional discrete algorithms or numerical approaches can only find a list of discrete points. The first author proposed in 2010 a new, elegant and accurate method, the geodesic-like method, for approximating geodesics on a regular surface. This paper will present b...

We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid Q that are cut out by algebraic surfaces in R. Such geodesics are either connected components of spatial elliptic curves or rational curves. Our approach is based on elements of the Weierstrass–Poncaré reduction theory for hyperelliptic tangential covers of elliptic curves and the addition...