Mechanical Structures on Lie Algebroids

Popescu, Liviu

doi:10.1007/s00009-018-1204-y

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…If so, a Lie algebroid is called integrable. We note that Lie algebroids have been studied widely by many authors, see: [25], [26], [35], [37] for instances.…”

Section: Preliminariesmentioning

confidence: 99%

Generalized symplectic Golden manifolds and Lie Groupoids

Şahin

2022

Filomat

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By considering the notion of Golden manifold and natural symplectic form on a generalized tangent bundle, we introduce generalized symplectic Golden structures on manifolds and obtain integrability conditions in terms of bivector fields, 2-forms, 1-forms and endomorphisms on manifolds and investigate isotropic subbundles. We also find certain relations between the integrability conditions of generalized symplectic Golden manifolds and Lie Groupoids which are important in mechanics as configuration space.

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“…If so, a Lie algebroid is called integrable. We note that Lie algebroids have been studied widely by many authors, see: [25], [26], [35], [37] for instances.…”

Section: Preliminariesmentioning

confidence: 99%

Generalized symplectic Golden manifolds and Lie Groupoids

Şahin

2022

Filomat

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“…Some aspects regarding the abnormality problem in control theory on Lie algebroids are presented in [23]. The link between optimal control and connection theory on Lie algebroids can be found in [24][25][26]. Lie geometric methods in control theory have been applied in many papers.…”

Section: Introductionmentioning

confidence: 99%

Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications

2022

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In the present paper, two optimal control problems are studied using Lie geometric methods and applying the Pontryagin Maximum Principle at the level of a new working space, called Lie algebroid. It is proved that the framework of a Lie algebroid is more suitable than the cotangent bundle in order to find the optimal solutions of some driftless control affine systems with holonomic distributions. Finally, an economic application is given.

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“…LaValle (2006) presented a unified treatment of control theory including holonomic and nonholonomic systems. Some type of control mechanical systems are investigated by Popescu (2018) or Khan, Akmeliawati & Khan (2018).…”

Section: Introductionmentioning

confidence: 99%

Applications of Driftless Control Affine Systems to a Problem of Inventory and Production

Popescu¹

2019

STUD INFORM CONTROL

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In this paper, the framework of driftless control affine systems has been used for the study of inventory and production problems. A mathematical model for an economic problem was built by using some optimal control techniques. For the controllability issue of the optimal control system, which involves restrictions on the final quantities required, the Lie geometric methods have been applied. In order to find the optimal solution, the Pontryagin Maximum Principle has been used at the level of a Lie algebroid, which in this case consists in an integrable distribution of the tangent space. Finally, a numerical example is presented.

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Mechanical Structures on Lie Algebroids

Cited by 3 publications

References 24 publications

Generalized symplectic Golden manifolds and Lie Groupoids

Generalized symplectic Golden manifolds and Lie Groupoids

Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications

Applications of Driftless Control Affine Systems to a Problem of Inventory and Production

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