A Control Problem with Passive Particles Driven by Point Vortices on the Sphere

Balsa, Carlos; Gama, S.

doi:10.1007/978-3-031-20319-0_11

Cited by 3 publications

(5 citation statements)

References 27 publications

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“…In spherical coordinates, the dynamics of the passive particle under control in identical conditions, as detailed in the preceding section, is determined by (see [19]):…”

Section: Modeling the Control Problem In Spherical Coordinatesmentioning

confidence: 99%

“…In a previous work [19], Equation ( 19) was employed to solve the control problem of displacing the passive particle between two specified points of the superficial sphere within a fixed time. However, a direct comparison of results with those obtained using Cartesian coordinates is not feasible due to inherent differences in controls, given that the controls are independent of each other.…”

Section: Modeling the Control Problem In Spherical Coordinatesmentioning

confidence: 99%

“…Here, y = (θ, ϕ) is the position of the passive particle described by Equation (19), U s = u θ , u ϕ is the control, and P 0 = (θ 0 , ϕ 0 ) and P f = (θ T , ϕ T ) are the initial and final point, respectively. The meaning of the objective function and constraints in the generic optimization problem P2 is identical to that in P1.…”

Section: Optimization Problemsmentioning

confidence: 99%

“…The discretization approach for the spherical optimization problem is analogous. The only difference is that the dynamics of the passive particle in each sub-interval are governed by Equation (19) in the case of Version 1, and by Equation (31) in the case of Version 2.…”

Section: Numerical Solutionsmentioning

confidence: 99%

“…A similar approach was implemented on the sphere in which the equations that govern the dynamics of the system composed of several vortices and a single passive particle were deduced using spherical coordinates [19]. It was observed that, in scenarios involving one, two, and three vortices, it is possible to show the existence of near or quasi-optimal trajectories for the passive particle.…”

Section: Introductionmentioning

confidence: 99%

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Exploring Controlled Passive Particle Motion Driven by Point Vortices on a Sphere

Balsa,

Otero-Espinar,

Gama

2024

Computation

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This work focuses on optimizing the displacement of a passive particle interacting with vortices located on the surface of a sphere. The goal is to minimize the energy expended during the displacement within a fixed time. The modeling of particle dynamics, whether in Cartesian or spherical coordinates, gives rise to alternative formulations of the identical problem. Thanks to these two versions of the same problem, we can assert that the algorithm, employed to transform the optimal control problem into an optimization problem, is effective, as evidenced by the obtained controls. The numerical resolution of these formulations through a direct approach consistently produces optimal solutions, regardless of the selected coordinate system.

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“…In spherical coordinates, the dynamics of the passive particle under control in identical conditions, as detailed in the preceding section, is determined by (see [19]):…”

Section: Modeling the Control Problem In Spherical Coordinatesmentioning

confidence: 99%

Section: Modeling the Control Problem In Spherical Coordinatesmentioning

confidence: 99%

Section: Optimization Problemsmentioning

confidence: 99%

Section: Numerical Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations