2019-12-07T22:12:15Z
https://digital.csic.es/dspace-oai/request
oai:digital.csic.es:10261/25910
2016-02-16T07:40:44Z
com_10261_87
com_10261_8
col_10261_340
2010-07-02T08:51:27Z
urn:hdl:10261/25910
Free polar motion of a triaxial and elastic body in Hamiltonian formalism: application to the Earth and Mars
Folgueira, M.
Souchay, J.
Solar System
Mars
Earth
Astronomy
Polar motion
The purpose of this paper is to show how to solve in Hamiltonian formalism the equations of the polar motion
of any arbitrarily shaped elastic celestial body, i.e. the motion of its rotation axis (or angular momentum) with respect to its
figure axis. With this aim, we deduce from canonical equations related to the rotational Hamiltonian of the body, the analytical
solution for its free polar motion which depends both on the elasticity and on its moments of inertia. In particular, we study
the influence of the phase angle δ, responsible for the dissipation, on the damping of the polar motion. In order to validate
our analytical equations, we show that, to first order, they are in complete agreement with those obtained from the classical
Liouville equations.
Then we adapt our calculations to the real data obtained from the polar motion of the Earth (polhody). For that purpose,
we characterize precisely the differences in radius J − χ and in angle l − θ between the polar coordinates (χ, θ) and (J, l)
representing respectively the motion of the axis of rotation of the Earth and the motion of its angular momentum axis, with
respect to an Earth-fixed reference frame, after showing the influence of the choice of the origin on these coordinates, and on the
determination of the Chandler period as well. Then we show that the phase lag δ responsible for the damping for the selected
time interval, between Feb. 1982 and Apr. 1990, might be of the order of δ ≈ 6◦, according to a numerical integration starting
from our analytical equations. Moreover, we emphasize the presence in our calculations for both χ and θ, of an oscillation with
a period TChandler/2, due to the triaxial shape of our planet, and generally not taken into account.
In a last step, we apply our analytical formulation to the polar motion ofMars, thus showing the high dependence of its damping
on the poorly known value of its Love number k. Moreover we emphasize the large oscillations of Mars’ polar motion due to
the triaxiality of this planet.
2010-07-02T08:51:27Z
2010-07-02T08:51:27Z
2005
artículo
Astronomy and Astrophysics - Les Ulis, 432 : 1101-1113 (2005)
0004-6361
http://hdl.handle.net/10261/25910
10.1051/0004-6361:20041312
eng
http://dx.doi.org/10.1051/0004-6361:20041312
openAccess
EDP Sciences