Symplectic connections and the linearisation of Hamiltonian systems
1991 ◽
Vol 117
(3-4)
◽
pp. 329-380
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Keyword(s):
SynopsisThis paper uses symplectic connections to give a Hamiltonian structure to the first variation equation for a Hamiltonian system along a given dynamic solution. This structure generalises that at an equilibrium solution obtained by restricting the symplectic structure to that point and using the quadratic form associated with the second variation of the Hamiltonian (plus Casimir) as energy. This structure is different from the well-known and elementary tangent space construction. Our results are applied to systems with symmetry and to Lie–Poisson systems in particular.
2017 ◽
Vol 1
(1)
◽
pp. 83
1998 ◽
Vol 08
(03)
◽
pp. 321-342
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Keyword(s):
2012 ◽
Vol 182-183
◽
pp. 1225-1229
2012 ◽
Vol 09
◽
pp. 285-292
2010 ◽
Vol 24
(05)
◽
pp. 587-597
◽
2010 ◽
Vol 53
(1)
◽
pp. 143-151