Variational problems on Riemannian manifolds with constrained accelerations
Optimization and Control
2022-02-25 v2 Mathematical Physics
math.MP
Abstract
We introduce variational problems on Riemannian manifolds with constrained acceleration and derive necessary conditions for normal extremals in the constrained variational problem. The problem consists on minimizing a higher-order energy functional, among a set of admissible curves defined by a constraint on the covariant acceleration. In addition, we use this framework to address the elastic splines problem with obstacle avoidance in the presence of this type of contraints.
Cite
@article{arxiv.2202.11600,
title = {Variational problems on Riemannian manifolds with constrained accelerations},
author = {Alexandre Anahory Simoes and Leonardo Colombo},
journal= {arXiv preprint arXiv:2202.11600},
year = {2022}
}