Theory of Orbits

Boccaletti, Dino; Pucacco, Giuseppe

doi:10.1007/978-3-662-03319-7

Cited by 89 publications

(77 citation statements)

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“…If l : m : n = 2 : 1 : 1, then the Hamiltonian also separates in the rotational parabolic and elliptic cylindrical coordinate systems [9], giving rise to additional conserved quantities and accidental degeneracy. However, if l+m+n > 4, then the Hamiltonian is still superintegrable [10,11,12], even though it now only separates in rectangular Cartesians. Further examples of systems which are superintegrable but not separable in more than one coordinate system include the Calogero-Moser problem [13,14] and the generalized Coulomb problem [15].…”

Section: Introductionmentioning

confidence: 99%

Superintegrability of the caged anisotropic oscillator

Evans

Verrier

2008

Journal of Mathematical Physics

107

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We study the Caged Anisotropic Harmonic Oscillator, which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l : m : n), but additionally with barrier terms describing repulsive forces from the principal planes. This confines the classical motion to a sector bounded by the principal planes, or cage. In 3 degrees, there are five isolating integrals of motion, ensuring that all bound trajectories are closed and strictly periodic. Three of the integrals are quadratic in the momenta, the remaining two are polynomials of order 2(l + m − 1) and 2(l + n − 1) . In the quantum problem, the eigenstates are multiply degenerate, exhibiting l 2 m 2 n 2 copies of the fundamental pattern of the symmetry group SU (3).PACS numbers:

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Section: Introductionmentioning

confidence: 99%

Superintegrability of the caged anisotropic oscillator

Evans

Verrier

2008

Journal of Mathematical Physics

107

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“…6) allows a better understanding of the meaning of the Lagrange points and of the path for the flow of the material from the secondary when it fills its Roche lobe. Recall that the L4 and L5 points are stable only in the case of a mass ratio M 2 /M 1 ≤ 0.0385 (Boccaletti & Pucacco 1996).…”

Section: Discussionmentioning

confidence: 99%

Physical parameters of the Algol system BP Muscae from simultaneous analysis of Geneva 7-colour light curves

Carrier

Barblan

Burki

et al. 2003

A&A

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Abstract. The semi-detached eclipsing binary system BP Muscae has been analysed using the Wilson-Devinney program. Light curves have been obtained in the G 7-colour photometric system, and radial velocity curves for both components have been measured with the spectrograph C. The physical and orbital parameters have been determined through a selfconsistent simultaneous solution of light curves in seven colours and of the radial velocity curves of both components. The absolute elements of the components are, for the primary (mass gainer), M 1 = 2.40 ± 0.01 M , R 1 = 2.64 ± 0.01 R , M bol 1 = 0.66 ± 0.04, T eff 1 = 9180 ± 90 K, and for the secondary (mass loser), M 2 = 0.68 ± 0.01 M , R 2 = 3.76 R , M bol 2 = 2.40 ± 0.08, T eff 2 = 5160 ± 90 K. The semi-major axis A of the relative orbit is 13.617 ± 0.019 R . The spectral type of the components are A0.5/1.5 V (primary) and about G5 III. The distance to BP Mus is evaluated as 562 ± 17 pc, and the colour excess E[B2-V1] as 0.220 ± 0.014.

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“…The tidal distortions generated by the secondary star of the CV are modeled by epicycles, a standard method of classical celestial mechanics (see Appendix A, and the review book by Boccaletti & Pucacco 1996). To study the evolution of each Fourier mode (labeled by k) of the velocity and of the enthalpy fluctuations obtained from a radial Fourier transformation of the equation of motion, we adopted the shearing sheet approximation (Goldreich & Lynden-Bell 1965;Julian & Toomre 1966;Goldreich & Tremaine 1978).…”

Section: Keplerian Accretion Flow Modelmentioning

confidence: 99%

“…The secondary, companion star is located at r = a, φ = 0, and z = 0. By applying the first-order epicyclic theory, we then obtain the steady-state displacements that describe the tidal distortion of the fluid streams corotating with the companion star (Goodman 1993;Boccaletti & Pucacco 1996).…”

Section: Keplerian Accretion Flow Modelmentioning

confidence: 99%

Floquet analysis of two-dimensional perturbed Keplerian flows in cataclysmic variables

Tamburini¹,

Bianchini²,

Franceschini³

2010

A&A

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Aims. We apply Floquet analysis to study the dynamical stability of two-dimensional axisymmetric Keplerian flows distorted by an m = 2 epicyclic periodic forcing term, representing a tidal perturbation in a thin accretion disk (AD) of a cataclysmic variable (CV). This tidal mode is responsible for the disk truncation mechanism. Methods. Floquet analysis reveals, with a positive Floquet exponent, exponentially growing modes of the local instabilities that can cause the disruption of the AD. The equations of the inviscid fluid used to model the AD describe an oversimplified two-dimensional tidally-distorted accretion disk. Viscosity and the other properties expected in a CV AD are taken from the Shakura-Sunyaev α-disk solution and introduced in the model through the thermodynamical quantities present in the equations. In particular, we address this investigation in search of parametric resonances of the radial Fourier components of the velocity field in the multi-dimensional parameter space of the solutions describing a fluid stream in a CV AD: the mass of the primary M 1 , the orbital period p of the system, the orbital fiducial radius r of the fluid stream and the normalized Fourier mode of the radial motion, k. Results. We find that, in region of the r3:2 orbital resonance radius, where superhumps (SH) form, the m = 2 tidal epicyclic modes alone would not introduce any perturbation in this region of the AD, and therefore the Floquet exponent of the m = 2 tidal force is found to be either negative or zero. However, only by introducing the 3:1 tidal perturbation, will the dynamics of the fluid streams at the SH radius become unstable indicating the onset of SH. Finally, Floquet analysis of the Fourier decomposition of the derivative along the radial x-direction shows the important role of the low Fourier modes of the radial velocity perturbations in the disk truncation mechanism.

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Theory of Orbits

Cited by 89 publications

References 0 publications

Superintegrability of the caged anisotropic oscillator

Superintegrability of the caged anisotropic oscillator

Physical parameters of the Algol system BP Muscae from simultaneous analysis of Geneva 7-colour light curves

Floquet analysis of two-dimensional perturbed Keplerian flows in cataclysmic variables

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