Construct · 3 fields · 3 citations
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In celestial mechanics libration is a slow oscillation back and forth about an equilibrium rather than a full circulation: the Moon's apparent rocking that lets us see slightly more than half its surface, and the resonant libration by which a body oscillates about a stable point of an orbital resonance or about a triangular Lagrange point. Murray and Dermott's Solar system dynamics treats these as bounded oscillations of an angle about a fixed value, with a libration amplitude and period. The referent is a confined oscillation about a dynamical equilibrium in an orbiting system, and it is the same construct that reappears, generalised, in phase-space dynamics and in a molecule's hindered rotation.[1]
In the dynamics of oscillating systems libration is bounded, back-and-forth motion about a stable equilibrium, contrasted with circulation, the unbounded motion that carries an angle all the way around. Goldstein, Poole, and Safko's Classical mechanics draws the distinction for a pendulum: below a critical energy it librates in an arc about the bottom, above it it circulates over the top, with the two regimes separated by a separatrix. It is the identical construct as the Moon's rocking or a Trojan asteroid's oscillation, stated generally for any system that trades between bounded oscillation and running motion.[2]
In molecular and condensed-matter physics libration is the hindered rotational oscillation of a molecule about its equilibrium orientation: a molecule held by its neighbours cannot spin freely, so it rocks within an angular well instead. Petersen, Møller, Rey, and Hynes's 2013 Ultrafast librational relaxation of H2O in liquid water tracks exactly this fast rocking of water molecules in the hydrogen-bond network. It is the same bounded-oscillation-about-equilibrium construct as orbital or pendulum libration, here realised in a molecule's orientation and measured in the far-infrared and terahertz band.[3]
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