Dissipation induced Instabilities and the Mechanical Laser

Marcel G. Clerc; Jerrold E. Marsden

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arXiv · nlin/0103049

Dissipation induced Instabilities and the Mechanical Laser

Marcel G. Clerc·Jerrold E. Marsden

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Abstract

We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allow us to show that a slightly pumping optical cavity is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. We display a simple mechanical system, close to the 1:1 resonance, which is a mechanical analog of the Laser.

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Marcel G. Clerc, Jerrold E. Marsden. 2001-03-26. Dissipation induced Instabilities and the Mechanical Laser. https://arxiv.org/abs/nlin/0103049

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