Abstract

OVANDO, Gabriela. Small oscillations on and Lie theory. Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.2, pp.115-123. ISSN 0041-6932.

Making use of Lie theory we propose a model for the simple harmonic oscillator and for the linear inverse pendulum of . In both cases the phase space are orbits of the coadjoint representation of the Heisenberg Lie group. These orbits and the Heisenberg Lie algebra are included in a solvable Lie algebra admitting an ad-invariant metric. The corresponding quadratic form induces the Hamiltonian and the associated Hamiltonian system is a Lax equation.

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