Is there a word or an idiom for lying on the bed peacefully and happy? Throwing yourself down on bed arms wide open, all your muscles relaxed and staring at the ceiling with a happy smile like something you dreamed of has just happened. Is there an idiom to narrow this situation?
There are a few terms which specifically capture the physical state of lying on the ground, face up, but they're fairly clinical and lack the mental overtones you describe (of complete relaxation, etc).
Supine: (of a person) lying face upward.
Which I like because its spelling reminds me of "supple" (relaxed, like a loose, floppy noodle). And there's also:
Recumbent: (especially of a person or human figure) lying down.
Which I like because it has hints of "recline" and "slumber".
Now, there are a couple of other words which are often used to mean lying on one's back, but in a strict technical sense, they actually mean lying face down:
Prostrate: lying stretched out on the ground with one's face downward
As a verb, prostrate¹ often carries an active connotation of laying face down in reverence or submission.
A more passive synonym, often used of the unconscious (e.g. boxers who have been knocked out) and corpses is:
Prone: lying flat, especially face downward.
This is the difference:
image credit: paramedicine.com
You'll notice that none of these words explicitly describe one's arms and legs being outstretched. Now, if you truly need to capture that physical arrangement, you can use:
spread-eagle: stretched out with one's arms and legs extended.
"prisoners are chained to their beds, spread-eagle, for days at a time"
But I strongly recommend you avoid that term.
If the actual physical arrangement of your body is less important than the mental state of relaxation you're trying to convey, then you can use my personal favorite word from this particular constellation²:
a state of rest, sleep, or tranquility.
"in repose her face looked relaxed"
a state of resting after exertion or strain
But again, that lacks the explicit physical state of laying flat on the floor.
So, if you need to capture both the physical and mental states, you can say something like "I was relaxing on the floor", or "I was just floating there" (metaphorically invoking the image of floating on water), or, heck, "I was so relaxed, I just gave myself up to gravity".
¹ Don't confuse prostrate and prostate (with only one
² Why do I like this particular word? Because I once read a wonderful short story about a living car, and one line the admiring narrator used to describe it was something like "*That car didn't park, it reposed.". Sadly, that's all I can remember of the story; its title is lost to me forever.
How about something based on the intransitive verb "loll?"
"Sit, lie, or stand in a lazy, relaxed way: 'the two girls lolled in their chairs'" --O.E.D.
"Scene four begins early the next morning with an indolent Stella, sexually satisfied and smug, lolling in bed." --[Bloom's Guides: Tennessee Williams's A Streetcar Named Desire, p. 40]
in a simile, could you use...?