I pinched myself to stop myself from falling asleep.

我掐自己以防自己睡着。

《牛津词典》

If the light is too bright, it can affect the speed of falling asleep.

光线太亮会影响入睡速度。

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If you have trouble falling asleep at night, take a daytime nap for less than 45 minutes and don't nap after 3 p.m. in the afternoon.

如果你晚上难以入睡，那么白天小睡要少于45分钟，下午3点以后不要小睡。

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Other products warn drivers if they are falling asleep or in danger of an accident.

VOA: special.2010.01.08

You start off with a transition period when you're falling asleep. We call that stage I.

一开始是过渡期,你开始进入睡眠状态，这是第一阶段。

耶鲁公开课 - 心理学导论课程节选

so I actually was like almost falling asleep in the second half, so you know.

我后半程几乎都快睡着了。

来伦敦旅游的 - SpeakingMax英语口语达人

The most common sleep problems in children are difficulty falling asleep and staying asleep and overall insufficient shut-eye.

WSJ: More Children With Sleep Problems Seek Overnight Tests

Sleep studies don't usually need to be done on children who have trouble falling asleep or staying asleep.

WSJ: More Children With Sleep Problems Seek Overnight Tests

By the third night, the babies were crying for a shorter period of time and falling asleep faster.

CNN: Should babies be allowed to 'cry it out'?