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arXiv · 2202.11600

Variational problems on Riemannian manifolds with constrained accelerations

Alexandre Anahory Simoes·Leonardo Colombo
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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.

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Alexandre Anahory Simoes, Leonardo Colombo. 2022-02-23. Variational problems on Riemannian manifolds with constrained accelerations. https://arxiv.org/abs/2202.11600

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