Read e-book online Dynamics of Small Solar System Bodies and Exoplanets PDF

By A. Lemaître (auth.), Jean J. Souchay, Rudolf Dvorak (eds.)

ISBN-10: 3642044573

ISBN-13: 9783642044571

This publication bargains an up to date review of present examine on Dynamics of Small sun method our bodies and Exoplanets. In course-tested huge chapters the authors conceal themes of theoretical celestial mechanics, physics and dynamics of asteroids, comets, balance of exoplanets and numerical integration codes utilized in dynamical astronomy.

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The first set (h, K , g) locates the position of the angular momentum vector G in an inertial frame of reference (the ecliptic plane at some epoch, for example); the second Euler’s set (g, J, l) locates the body frame (the axis of inertia) in the Fig. 26 The linked sets of Euler angles (l, K , g) and (g, J, h) from which the Andoyer’s angular variables are defined. They locate the body frame (f1 , f2 , f3 ) with respect to the inertial frame (e1 , e2 , e3 ) Resonances: Models and Captures 47 previous frame tied to the angular momentum.

1 Formulation and Scaling The first model of resonance is the pendulum, as already mentioned in (11); in celestial mechanics cases (development of the third body perturbation, spin–orbit 22 A. Lemaˆıtre resonance, geostationary resonances), it is generally given first in the following Hamiltonian form: H(σ, S) = αS 2 + β S + cos(σ − σ0 ). We introduce a change of phase to make σ0 disappear (r = σ − σ0 ) and a translation on S to get rid of the linear term: R = S − S0 . H becomes H(r, R) = α (R + S0 )2 + β (R + S0 ) + cos r = α R 2 + 2α R S0 + αS02 + β R + β S0 + cos r = α R 2 + cos r + C0 , β .

T The Hamiltonian writes K(Ψ, J, δ) = H (σ (Ψ, J, δ), S(Ψ, J, δ), δ) ∂F = K (−, J, δ) + ∂t ∂F (Ψ, J, δ) = K (−, J, δ) + δ˙ ∂δ and is associated to the dynamics: ∂K ∂K = + O(η) Ψ˙ = ∂J ∂J and ∂K J˙ = − = O(η). ∂Ψ We can conclude that for small η the area J is quasi-constant, as long as we avoid the separatrices regions, and for times smaller than η1 . We follow the behavior of the dynamical system by the help of a guiding trajectory, the area of which is quasi-constant; δ is slowly changing with time, but at each time we fix its value and calculate the enclosed area, we get a quasi-constant quantity (with variations smaller than η for times smaller than η1 ).

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Dynamics of Small Solar System Bodies and Exoplanets by A. Lemaître (auth.), Jean J. Souchay, Rudolf Dvorak (eds.)

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