Relaxing Nonholonomic Constraints

Rand, Richard H.; Ramani, D. V.

doi:10.1142/9789812792518_0025

Cited by 6 publications

(5 citation statements)

References 1 publication

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“…Our model for the nonholonomic constraint, which respects the Lagrange-D'Alembert principle, has been considered in the aerospace engineering community [23], while robotic models for underwater vehicles taking into account the effects of circulation were considered in [15].…”

Section: Introduction and Outlinementioning

confidence: 99%

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

Fedorov¹,

García-Naranjo²,

Vankerschaver³

2013

Discrete &Amp; Continuous Dynamical Systems - A

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We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles.The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.

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Section: Introduction and Outlinementioning

confidence: 99%

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

Fedorov¹,

García-Naranjo²,

Vankerschaver³

2013

Discrete &Amp; Continuous Dynamical Systems - A

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“…Следует иметь в виду, что неголономная модель движения твердого тела также использует-ся для описания движения твердого тела в жидкости, например, в [37] -для изучения падения диска в сопротивляющейся среде (без учета парашютирования), в [76] -для падения пластин-ки. В [74] неголономная модель падения упомянута в связи с движением в жидкости снарядов с оперением, причем предполагается, что центр масс твердого тела может перемещаться внутри него по заданному закону.…”

Section: сани чаплыгина на наклонной плоскости в поле тяжестиunclassified

“…Однако такая модель (вопреки точке зрения, высказанной в [37]) на самом деле не связана с эффектами парашютирования и не от-ражает правильно физические механизмы взаимодействия твердого тела и жидкости (см. так-же [74,76]). …”

Section: сани чаплыгина на наклонной плоскости в поле тяжестиunclassified

Asymptotic stability and associated problems of dynamics of falling rigid body

2007

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“…It is an interesting historic coincidence that the name of Chaplygin is linked both to the development of the Chaplygin-Lamb equations [4] as well as to the nonholonomic Chaplygin sleigh [5]. Similar models for two-dimensional swimmers have been studied in [12] (see also [23]). The motion of the hydrodynamic Chaplygin sleigh in the presence of circulation is treated in [7].…”

Section: Introduction and Outlinementioning

confidence: 99%

Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation

García-Naranjo

Vankerschaver

2013

Journal of Geometry and Physics

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We consider nonholonomic systems whose configuration space is the central extension of a Lie group and have left invariant kinetic energy and constraints. We study the structure of the associated Euler-Poincaré-Suslov equations and show that there is a one-to-one correspondence between invariant measures on the original group and on the extended group. Our results are applied to the hydrodynamic Chaplygin sleigh, that is, a planar rigid body that moves in a potential flow subject to a nonholonomic constraint modeling a fin or keel attached to the body, in the case where there is circulation around the body.

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Relaxing Nonholonomic Constraints

Cited by 6 publications

References 1 publication

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

Asymptotic stability and associated problems of dynamics of falling rigid body

Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation

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