<i>Classical Dynamics: Modern Perspective</i>

Sudarshan, E. C. G.; Mukunda, N.; Newton, Roger G.

doi:10.1063/1.3069162

Cited by 236 publications

(434 citation statements)

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“…The charged heavy top, also introduced in this paper, is a heavy top [1][2][3] immersed in an electric field. The bracket for the charged heavy top arises from a semidirect product of SO (3) and R 3 × R 3 .…”

Section: Introductionmentioning

confidence: 99%

The twisted top

Thiffeault¹,

Morrison²

2001

Physics Letters A

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We describe a new type of top, the twisted top, obtained by appending a cocycle to the Lie-Poisson bracket for the charged heavy top, thus breaking its semidirect product structure. The twisted top has an integrable case that corresponds to the Lagrange (symmetric) top. We give a canonical description of the twisted top in terms of Euler angles. We also show by a numerical calculation of the largest Lyapunov exponent that the Kovalevskaya case of the twisted top is chaotic.

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Section: Introductionmentioning

confidence: 99%

The twisted top

Thiffeault¹,

Morrison²

2001

Physics Letters A

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“…For generic dependence of the form F (κ 1 ) the model is just reparametrization invariant. A new gauge symmetry appears though for the particular case of linear dependence [4][5] 13) which is also invariant under rigid scale transformations x → λx. It was shown in [6] that these two gauge transformations give a realization of the W 3 symmetry algebra.…”

Section: The Orthogonality Conditions On X (I)mentioning

confidence: 99%

“…If any of the primary constraints should become second-class during the stabilization procedure, the associated coefficient λ i would take a definite canonical form [13].…”

Section: The Orthogonality Conditions On X (I)mentioning

confidence: 99%

“…The requirement of stability of these constraints upon evolution (i .e.φ i ≈ 0) usually brings in new sets of constraints, which might turn some of the primary constraints into second-class. The actual number of independent gauge transformations is given by the number of primary constraints that remain first-class after the stabilization procedure [13].…”

Section: The Orthogonality Conditions On X (I)mentioning

confidence: 99%

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Extended gauge invariance in geometrical particle models and the geometry of W-symmetry

Ramos

Roca

1995

Nuclear Physics B

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We prove that particle models whose action is given by the integrated n-th curvature function over the world line possess n + 1 gauge invariances. A geometrical characterization of these symmetries is obtained via Frenet equations by rephrasing the n-th curvature model in R d in terms of a standard relativistic particle in S d−n . We "prove by example" that the algebra of these infinitesimal gauge invariances is nothing but W n+2 , thus providing a geometrical picture of the W-symmetry for these models. As a spin-off of our approach we give a new global invariant for four-dimensional curves subject to a curvature constraint. †

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“…Some focus more on systems with a finite number of degrees of freedom [41], others on field theories [28] and some on both [42,25,29]. For generally covariant theories you may consult [24].…”

Section: Introductionmentioning

confidence: 99%

Hamilton's formalism for systems with constraints

Wipf¹

Lecture Notes in Physics

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Classical Dynamics: Modern Perspective

Cited by 236 publications

References 0 publications

The twisted top

The twisted top

Extended gauge invariance in geometrical particle models and the geometry of W-symmetry

Hamilton's formalism for systems with constraints

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