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Variational problems on Riemannian manifolds with constrained accelerations (2202.11600v2)
Published 23 Feb 2022 in math.OC, math-ph, and 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.
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