Non-linear dynamics of a hanging rope

Fritzkowski, Paweł; Kamiński, Henryk

doi:10.1590/s1679-78252013000100008

Cited by 5 publications

(1 citation statement)

References 7 publications

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“…For the modeling framework, we refer to the survey [28] for an introduction on the derivation of equations for inextensible strings (with no curvature constraints) and their discrete counterpart, the chains. The papers [8,9] treat the same topic, stressing the numerical aspects of the problem. The paper [22] provides a nice investigation of boundary conditions for the Euler's dynamic elastica and presents some numerical simulations -also, see the paper [2] for a discussion of the discrete case.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Optimal Control of an Octopus Tentacle

Cacace¹,

Lai²,

Loreti³

2020

SIAM J. Control Optim.

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We present a control model for an octopus tentacle, based on the dynamics of an inextensible string with curvature constraints and curvature controls. We derive the equations of motion together with an appropriate set of boundary conditions, and we characterize the corresponding equilibria. The model results in a system of fourth-order evolutive nonlinear controlled PDEs, generalizing the classic Euler's dynamic elastica equation, that we approximate and solve numerically introducing a consistent finite difference scheme. We proceed investigating a reachability optimal control problem associated to our tentacle model. We first focus on the stationary case, by establishing a relation with the celebrated Dubins' car problem. Moreover, we propose an augmented Lagrangian method for its numerical solution. Finally, we address the evolutive case obtaining first order optimality conditions, then we numerically solve the optimality system by means of an adjoint-based gradient descent method.

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