Constrained Lepage forms

Krupková, Olga; Volna, Jana; Volný, Petr

doi:10.1142/9789812790613_0052

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Geometrical Theory Of Nonholonomic Mechanical Systems1

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2018

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“…Key geometrical objects adapted to the fibred structure are sections and their jet prolongations, projectile and vertical vector fields, as well as horizontal and contact differential forms. The detailed theoretical background can be noted in (Krupková, 1998).…”

Section: Geometrical Theory Of Nonholonomic Mechanical Systemsmentioning

confidence: 99%

Archives of Control Sciences

Haddout¹,

Guennoun²,

Chen³

2018

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In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a Forklift-truck robot motion. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. On the other hand, the equations of motion of a Forklift-truck robot are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented.

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Section: Geometrical Theory Of Nonholonomic Mechanical Systemsmentioning

confidence: 99%