The three laws are already very simple and basic, is there any way to reduce them further?
Well, in a way the first law follows from the second law. In reality Newtons laws don't stand on their own. You have already made a lot of assumptions about the vector addition of forces, the mathematical structure of the space, the properties of rigid bodies. So if you put more work into the definition of these things, you might be able to get the essence of Newton's laws in a simpler expression, but I think they are good the way they are.
I don't think it's fair to say that the first law follows from the second law. In fact, the second law doesn't make sense without the first law. The second law says that F=ma in a inertial reference frame. This law can be totally vacuous if there are not inertial frames in the first place. That's what the first law is for.
Technically the first law doesn't say anything about your frame, it just describes the existence of other inertial frames.
There is also the Lagrangian formulation (i.e. extremising the action). But whether this is 'simpler' than Newton's laws is a personal preference, I think. I personally think it is simpler than Newton's laws.
worth remembering that when you first meet Newton's laws the first law states that in the absence of a resultant force an object is either at rest or moving with constant velocity.
The second law tells you that in the presence of a resultant force the object cannot be at rest or moving with constant velocity i.e it must be accelerating.
laws 1 and 2 go together beautifully as one.
nice, I hadn't realized that before.
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