A variational principle for Moledensky’s liquid-core problem

Moritz, Helmut

doi:10.1007/bf02525735

Cited by 16 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this way, as pointed out by Moritz [1982], the treatment of the problem is very elegant and symmetric and to some extent independent of the nature of the layer. It should be noted that.…”

mentioning

confidence: 88%

“…In our theory, by means of a Hamiltonian formalism, we only need to compute the kinetic energy in a canonical set, without requiring the expression of the internal torques, which arises in a natural •nanner. That is the advantage expected from a variational method, as pointed out by Moritz [1982].…”

Section: Polar Motionmentioning

confidence: 99%

“…of parameters, which could be computed from geophysical Earth models or properly fitted to the observations. Finally, another method is to approach the problem using the variational theories of classical mechanics [e.g., Poincar•, 1910;Vicente, 1957a, 1957b;Kubo, 1979;Moritz, 1982;Getino and Ferrdndiz, 1998c] as in this investigation. As it is well known, the variational methods and the vectorial methods are almost equivalent because they are based on ahnost overlapping physical principles.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Canonical approach to the free nutations of a three‐layer Earth model

Escapa¹,

Getino²,

Ferrándiz³

2001

J. Geophys. Res.

View full text Add to dashboard Cite

mentioning

confidence: 88%

Section: Polar Motionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Canonical approach to the free nutations of a three‐layer Earth model

Escapa¹,

Getino²,

Ferrándiz³

2001

J. Geophys. Res.

View full text Add to dashboard Cite

“…Þmeans that an appropriate definition of the core rotation (MORITZ 1982) has been made, so that it is referred to a Tisserand frame (MORITZ 1982), as detailed in GETINO (1995). The kinetic energy is thus…”

Section: Effect Of the Liquid Corementioning

confidence: 99%

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

Ferrándiz

Navarro

Escapa

et al. 2014

Pure Appl. Geophys.

View full text Add to dashboard Cite

“…(2) Thus, it is known that the relative angular momentum of the small residual velocity due to the effects of non-sphericity can be made zero with an appropriate definition of the core rotation (Moritz 1982), or by taking the Tisserand axes as the core-fixed frame (Moritz 1984), as detailed in Getino (1995a).…”

Section: The R I G I D Mantle-liquid-core Earth Modelmentioning

confidence: 99%

A Hamiltonian approach to dissipative phenomena between the Earth's mantle and core, and effects on free nutations

Getino¹,

Ferrándiz

1997

Geophysical Journal International

View full text Add to dashboard Cite

S U M M A R YThe Hamiltonian formalism was recently applied by Getino (1995a,b) for the study of the rotation of a non-rigid earth with a heterogeneous and stratified liquid core. That earth model is generalized here by including the effect of the dissipation arising from the mantle-core interaction, using a model similar to that of Sasao, Okubo 8z Saito (1980), which includes both viscous and electromagnetic coupling. First, a solution for the free nutations is obtained following a classical approach, which in our opinion is more familiar to most of the readers than the Hamiltonian treatment. This solution provides a theoretical basis clear enough to study both the qualitative and quantitative effects of the dissipations considered in the hypotheses. The main qualitative features are, besides the delays, that the free core nutation (FCN) suffers an exponential damping, while the chandler wobble (CW) is not damped at first order, by the dissipation considered. The numerical values obtained for the complex compliances agree with the most recent experimental computations.Next, the problem is studied under a Hamiltonian formalism, and a solution equivalent to the above is obtained. Besides its interest from a theoretical point of view, this formalism is necessary in order to apply canonical perturbation methods in order to obtain analytical nutation series.

show abstract

A variational principle for Moledensky’s liquid-core problem

Cited by 16 publications

References 14 publications

Canonical approach to the free nutations of a three‐layer Earth model

Canonical approach to the free nutations of a three‐layer Earth model

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A Hamiltonian approach to dissipative phenomena between the Earth's mantle and core, and effects on free nutations

Contact Info

Product

Resources

About