Vol 1 - L D Landau, E.M. Lifshitz - Mechanics · Problem 1

Small Oscillations

Physics — Landau & Lifshitz · oscillations-two-degrees-of-freedom-coupled

Problem

Determine the oscillations of a system with two degrees of freedom whose Lagrangian is L=12(x˙2+y˙2)−12ω02(x2+y2)+αxyL = \frac{1}{2}(\dot{x}^2+\dot{y}^2)-\frac{1}{2}\omega_0^2(x^2+y^2)+\alpha xy (two identical one-dimensional systems of eigenfrequency ω0\omega_0 coupled by an interaction −αxy-\alpha xy).

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