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How to rotate around an axis so that another axis always points down? (see images)

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I'm using LookAt() to make characters look at things (like the camera). However, the more their body is turned away from the object, the more their head tilts strangely instead of always keeping the X axis down. How would I keep the X axis always pointing downward to avoid the head tilting strangely like that? ![alt text][1] [1]: /storage/temp/161657-figure-1-3.jpg

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