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The Triaxiality Role in the Spin-Orbit Dynamics of a Rigid Body

A. Cantero

A. Cantero

DITEC, Facultad de Informática, Universidad MurciaMurcia, Spain
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Cantero, A.
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F. Crespo

F. Crespo

GISDA, Dept. de Matemática, Facultad de Ciencias, Universidad del Bío-BíoConcepción, Chile
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Crespo, F.
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S. Ferrer

S. Ferrer

DITEC, Facultad de Informática, Universidad MurciaMurcia, Spain
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Ferrer, S.
  
Oct 03, 2018
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Published Online: Oct 03, 2018
Page range: 187 - 208
Received: Feb 06, 2018
Accepted: May 21, 2018
DOI: https://doi.org/10.21042/AMNS.2018.1.00015
Keywords
© 2018 A. Cantero et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Geometry of the variables (r, φ, ψ, θ, δ, ν, R, Φ, Ψ, Θ, Δ, N). The variable r and the angles are explicitly given in the figure, while the associated momenta are included implicitly through the inclinations of the planes. The conjugate variable R remains unrepresented because of its pure dynamical sense.
Geometry of the variables (r, φ, ψ, θ, δ, ν, R, Φ, Ψ, Θ, Δ, N). The variable r and the angles are explicitly given in the figure, while the associated momenta are included implicitly through the inclinations of the planes. The conjugate variable R remains unrepresented because of its pure dynamical sense.

Fig. 2

Columns from left to right we have: (i)ρ = 0, A1 = 9.80 · 1020, A2 = 9.8 · 1020, A3 = 1.07 · 1021. (ii)ρ = 0.0005, A1 = 1.17 · 1021, A2 = 1.23 · 1021, A3 = 1.39 · 1021. Abscissas are orbital periods and D[x] = xFull–xIntermediary. The orbital period is 10.8 hours and r is expressed in Km, which initially is set to 1.560 Km.
Columns from left to right we have: (i)ρ = 0, A1 = 9.80 · 1020, A2 = 9.8 · 1020, A3 = 1.07 · 1021. (ii)ρ = 0.0005, A1 = 1.17 · 1021, A2 = 1.23 · 1021, A3 = 1.39 · 1021. Abscissas are orbital periods and D[x] = xFull–xIntermediary. The orbital period is 10.8 hours and r is expressed in Km, which initially is set to 1.560 Km.

Fig. 3

Columns from left to right we have: (i)ρ = 0, A1 = 9.80 · 1020, A2 = 9.8 · 1020, A3 = 1.07 · 1021. (ii)ρ = 0.15, A1 = 1.17 · 1021, A2 = 1.23 · 1021, A3 = 1.39 · 1021. (iii)ρ = 0.35, A1 = 1.06 · 1021, A2 = 1.18 · 1021, A3 = 1.28 · 1021. Abscissas are orbital periods and D[x] = xFull–xIntermediary. The orbital period is 10.8 hours and r is expressed in Km, which initially is set to 1.560 Km.
Columns from left to right we have: (i)ρ = 0, A1 = 9.80 · 1020, A2 = 9.8 · 1020, A3 = 1.07 · 1021. (ii)ρ = 0.15, A1 = 1.17 · 1021, A2 = 1.23 · 1021, A3 = 1.39 · 1021. (iii)ρ = 0.35, A1 = 1.06 · 1021, A2 = 1.18 · 1021, A3 = 1.28 · 1021. Abscissas are orbital periods and D[x] = xFull–xIntermediary. The orbital period is 10.8 hours and r is expressed in Km, which initially is set to 1.560 Km.

Fig. 4

Left column e = 0.1 and right column e = 0.5.Abscissas are orbital periods and D[x] = xFull–xIntermediary. The orbital period is 10.8 hours and r is expressed in Km, which initially is set to 1.560 Km.
Left column e = 0.1 and right column e = 0.5.Abscissas are orbital periods and D[x] = xFull–xIntermediary. The orbital period is 10.8 hours and r is expressed in Km, which initially is set to 1.560 Km.

Fig. 5

Left column (H = 1000Km, T = 22.8h) and right column (H = 2000Km, T = 10.8h), where T is the orbital period expressed in hours. Abscissas are orbital periods and D[x] = xFull–xIntermediary
Left column (H = 1000Km, T = 22.8h) and right column (H = 2000Km, T = 10.8h), where T is the orbital period expressed in hours. Abscissas are orbital periods and D[x] = xFull–xIntermediary

Fig. 6

(Left) triaxiality region with τ1 = 0.35 and τ2 = 0.9. (Right) Curves cσ1 and cσ2 restricted to interval [0, 1] for ζ = 0.7.
(Left) triaxiality region with τ1 = 0.35 and τ2 = 0.9. (Right) Curves cσ1 and cσ2 restricted to interval [0, 1] for ζ = 0.7.

Fig. 7

Parameters: ζ = 0.2, τ1 = 0.3, τ2 = 0.75.
Parameters: ζ = 0.2, τ1 = 0.3, τ2 = 0.75.

Fig. 8

Parameters: ζ = 0.2, τ1 = 0.6, τ2 = 0.75.
Parameters: ζ = 0.2, τ1 = 0.6, τ2 = 0.75.

Fig. 9

Special relative equilibria of the body-perpendicular type with ν = ±nπ.
Special relative equilibria of the body-perpendicular type with ν = ±nπ.

Fig. 10

Special relative equilibria of the body-inclined type.
Special relative equilibria of the body-inclined type.

Fig. 11

Spherical triangles involved in the problem. α is the angle between the two nodes of the orbital plane. (a) Triangle formed by the orbital angular momentum plane, the total angular momentum plane and the reference plane. (b) Triangle formed by the rotational angular momentum plane, the total angular momentum plane and the reference plane.
Spherical triangles involved in the problem. α is the angle between the two nodes of the orbital plane. (a) Triangle formed by the orbital angular momentum plane, the total angular momentum plane and the reference plane. (b) Triangle formed by the rotational angular momentum plane, the total angular momentum plane and the reference plane.
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