The Non-Holonomic Mechanics

Kupka, Ivan; Oliva, Waldyr M.

doi:10.1006/jdeq.2000.3897

Cited by 29 publications

(38 citation statements)

References 6 publications

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“…We remark that the constrained dynamics formulated above is the classical one which is also called d'Alembertian [24] as opposed to the recently proposed vakonomic constrained dynamics [23].…”

Section: Accepted Manuscript 6 Special Forms Of the Lmentioning

confidence: 92%

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On the general form of the law of dynamics

Romano

Barretta

Diaco

2009

International Journal of Non-Linear Mechanics

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The dynamics of Lagrangian systems is formulated with a differential geometric approach and according to a new paradigm of the calculus of variations. Discontinuities in the trajectory, non-potential force systems and linear constraints are taken into account with a coordinate-free treatment. The law of dynamics, characterizing the trajectory in a general non-linear configuration manifold, is expressed in terms of a variational principle and of differential and jump conditions. By endowing the configuration manifold with a connection, the generallaw is shown to be tensorial in the velocity of virtual flows and to depend on the torsion of the connection. This result provides a general expression of the EULER–LAGRANGE operator. POINCARÉ and LAGRANGE forms of the law are recovered as special cases corresponding, respectively, to the connection induced by natural and mobile reference frames. For free motions, the geodesic property of the trajectory is directly inferred by adopting the LEVI-CIVITA connection induced by the kinetic energy

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Section: Accepted Manuscript 6 Special Forms Of the Lmentioning

confidence: 92%

“…Introducing in the Whitney sum Δ Γ ⊕Δ ⊥ Γ the tensorial Weingarten map: W(u, v) := Π ⊥ (∇ u v) , we may write the law of motion for a perfect dynamical system as in [3,24]:…”

Section: Accepted Manuscript 6 Special Forms Of the Lmentioning

confidence: 99%

On the general form of the law of dynamics

Romano

Barretta

Diaco

2009

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

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“…General necessary and sufficient conditions for the conservation of volume for both latter cases have been reported in [27] and [36] (see also [43]). …”

Section: A Gma Invariant Measurementioning

confidence: 93%

“…For more details, we refer the reader to [36] (concerning the formulation of d'Alembert-Chetaev mechanics for nonlinearly constrained mechanical systems) and to [27] (for linearly constrained systems).…”

Section: Basic Notations and Definitionsmentioning

confidence: 99%