Journal of Dynamical and Control Systems, Jun 22, 2021
This paper is the second part of a study initiated by Mortada et al. (2020), where we have consid... more This paper is the second part of a study initiated by Mortada et al. (2020), where we have considered the rolling (or development) of two Riemannian connected manifolds (M,g) and $(\hat {M},\hat {g})$ of dimensions 2 and 3, respectively, with the constraints of no-spinning and no-slipping. In the work of Mortada et al. (Acta Appl Math, 139:105131, 2015), the general setting of the rolling of two Riemannian connected manifolds with different dimensions has been modeled as a driftless control affine system on a fibered space Q of dimension eight with special attention on understanding the local structure of the rolling orbits, i.e., the reachable sets in Q. In the present paper, we pursue our investigations on the structure of non-open orbits and we precisely describe the second possible local structure of rolling orbits of dimension 5.
Journal of Dynamical and Control Systems, Jun 22, 2021
This paper is the second part of a study initiated by Mortada et al. (2020), where we have consid... more This paper is the second part of a study initiated by Mortada et al. (2020), where we have considered the rolling (or development) of two Riemannian connected manifolds (M,g) and $(\hat {M},\hat {g})$ of dimensions 2 and 3, respectively, with the constraints of no-spinning and no-slipping. In the work of Mortada et al. (Acta Appl Math, 139:105131, 2015), the general setting of the rolling of two Riemannian connected manifolds with different dimensions has been modeled as a driftless control affine system on a fibered space Q of dimension eight with special attention on understanding the local structure of the rolling orbits, i.e., the reachable sets in Q. In the present paper, we pursue our investigations on the structure of non-open orbits and we precisely describe the second possible local structure of rolling orbits of dimension 5.
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