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hypernihl

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**Coordinate System of Coupled Oscillators and "4D" Phase Space representation**

So, I've modeled the interaction between two cantilever beams with the kinetic and potential energies shown in the above figure. The cantilevers are very stiff and have a small oscillation amplitude, so they can be modeled as two interacting springs. In the coupling potential epsilon and N > 0.

I'm having a little trouble wrapping my head around the "signs (+ or -)" in the equations of motion derived from the Lagrangian.

Have I set this up right?

All so, I have been displaying the phase-space by potting v1+v2 vs d-(x1+x2).

I'd appreciate any thoughts on this.

Thanks