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Separatrix (mathematics)

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A separatrix refers to the boundary separating two modes of behaviour in a differential equation. For example, consider the differential equation describing the motion of a pendulum:

${d^{2}\theta \over dt^{2}}+{g \over l}\sin \theta =0$ .

The separatrix marks the transition between pendulum motion and rotation.

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Separatrix from MathWorld

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