A system with constraints in the nambu mechanics

Homma, Teiichi; Kadoya, Morihiro

doi:10.1007/bf02874413

Cited by 2 publications

(4 citation statements)

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“…We are not pretending to present the complete formal extension of the Nambu formalism, but the reader is referred to the literature for reviews on the topic. Some examples of other real physical systems described by Nambu's formalism (as well as proposals for quantised versions of Nambu dynamics) can be found in [2,3,4,6,7,10,11,12,13,14,15]. We start by briefly reviewing the main ideas within Nambu formalism.…”

Section: Copyright C 2007 By a Molgado And A Rodríguezmentioning

confidence: 99%

“…¿From this last generalisation it can be seen that the Hamiltonian formalism is contained in Nambu's formalism as a special case, namely, a two-dimensional phase space and a single Hamiltonian function. For further relations between Nambu and Hamiltonian formalisms, the reader is referred to [3,7,10]. The rest of the paper is as follows.…”

Section: Copyright C 2007 By a Molgado And A Rodríguezmentioning

confidence: 99%

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Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Molgado

Rodríguez

2007

Journal of Nonlinear Mathematical Physics

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In this work we investigate a formal mapping between the dynamical properties of the unidimensional relativistic oscillator and the asymmetrical rigid top at a classical level. We study the relativistic oscillator within Yamaleev's interpretation of Nambu mechanics. Such interpretation is based on the factorisation of the momenta, and as a consequence of this factorisation we are led to a three dimensional phase space. Solutions of the relativistic oscillator are given in terms of the Jacobian elliptic functions and hence we establish a correspondence of these solutions in terms of well known quantities from the rigid body theory. We also study some mechanical restrictions that appear in the mathematical development of the mapping. In particular, we find a lower bound for the relativistic frequency in order to make the mapping self-consistent and physically legitimate.

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Section: Copyright C 2007 By a Molgado And A Rodríguezmentioning

confidence: 99%

Section: Copyright C 2007 By a Molgado And A Rodríguezmentioning

confidence: 99%

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Molgado

Rodríguez

2007

Journal of Nonlinear Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Some examples of other real physical systems described by Nambu's formalism (as well as proposals for quantised versions of Nambu dynamics) can be found in [2,3,4,6,7,10,11,12,13,14,15]. We start by briefly reviewing the main ideas within Nambu formalism.…”

confidence: 99%

“…For further relations between Nambu and Hamiltonian formalisms, the reader is referred to [3,7,10]. The rest of the paper is as follows.…”

confidence: 99%

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Molgado¹,

Rodríguez²

2007

JNMP

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A system with constraints in the nambu mechanics

Cited by 2 publications

References 5 publications

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

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