Geodesic
Hamilton–Jacobi Theory and Moving Frames
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The interplay between the Hamilton–Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.
Keywords: Hamilton–Jacobi theory; orthogonal separable coordinates; Killing tensors; group action; moving frame map; regular foliation. 
@article{SIGMA_2007_3_a69,
     author = {Joshua D. MacArthur and Raymond G. McLenaghan and Roman G. Smirnov},
     title = {Hamilton{\textendash}Jacobi {Theory} and {Moving} {Frames}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a69/}
}
TY  - JOUR
AU  - Joshua D. MacArthur
AU  - Raymond G. McLenaghan
AU  - Roman G. Smirnov
TI  - Hamilton–Jacobi Theory and Moving Frames
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2007
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a69/
LA  - en
ID  - SIGMA_2007_3_a69
ER  - 
%0 Journal Article
%A Joshua D. MacArthur
%A Raymond G. McLenaghan
%A Roman G. Smirnov
%T Hamilton–Jacobi Theory and Moving Frames
%J Symmetry, integrability and geometry: methods and applications
%D 2007
%V 3
%U http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a69/
%G en
%F SIGMA_2007_3_a69
Joshua D. MacArthur; Raymond G. McLenaghan; Roman G. Smirnov. Hamilton–Jacobi Theory and Moving Frames. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a69/

[1] Benenti S., “Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation”, J. Math. Phys., 38 (1997), 6578–6602 | DOI | MR | Zbl

[2] Eisenhart L. P., “Separable systems of Stäckel”, Ann. Math., 35 (1934), 284–305 | DOI | MR

[3] Fels M., Olver P. J., “Moving coframes. I. A practical algorithm”, Acta. Appl. Math., 51 (1998), 161–213 | DOI | MR

[4] Fels M., Olver P. J., “Moving coframes. II. Regularization and theoretical foundations”, Acta. Appl. Math., 55 (1999), 127–208 | DOI | MR | Zbl

[5] Horwood J. T., McLenaghan R. G., Smirnov R. G., “Invariant classification of orthogonal separable Hamiltonian systems in Euclidean space”, Comm. Math. Phys., 221 (2005), 679–709 ; math-ph/0605023 | DOI | MR

[6] Kuznetsov V. B., “Simultaneous separation for the Kowalevski and Goryachev–Chaplygin gyrostats”, J. Phys. A: Math. Gen., 35 (2002), 6419–6430 ; nlin.SI/0201004 | DOI | MR | Zbl

[7] MacArthur J. D., The equivalence problem in differential geometry, MSc thesis, Dalhousie University, 2005

[8] McLenaghan R. G., Smirnov R. G., The D., “Group invariant classification of separable Hamiltonian systems in the Euclidean plane and the $O(4)$-symmetric Yang–Mills theories of Yatsun”, J. Math. Phys., 43 (2002), 1422–1440 | DOI | MR | Zbl

[9] McLenaghan R. G., Smirnov R. G., The D., “An extension of the classical theory of invariants to pseudo-Riemannian geometry and Hamiltonian mechanics”, J. Math. Phys., 45 (2004), 1079–1120 | DOI | MR | Zbl

[10] Olver P. J., Classical invariant theory, Student Texts, 44, London Mathematical Society, Cambridge University Press, 1999 | MR

[11] Palais R. S., A global formulation of the Lie theory of transportation groups, Memoirs Amer. Math. Soc., no. 22, AMS, Providence, R.I., 1957 | MR

[12] The D., Notes on complete sets of group-invariants in $\mathcal K^2(\mathbb R^2)$ and $\mathcal K^3(\mathbb R^2)$, unpublished, 2004