If the bike is even close to fitting you correctly, you should find the bike to be MORE stable with your hands on the drops, or on top of the brake hoods (nice, relaxed grip, like a bird's feet on a perch). Steering from the tops gives you a place to relax and sit up a little, to look around or behind you, or grab water bottles, or spray dogs etc.
It will take getting used to. Try putting your hands on the "elbows" of the drops, where you can reach the brake levers.
It should feel about the same as holding the brake hoods. If it hurts your back, or you feel hunched over (seat pinching you?) probably raising the stem or tilting the seat forward 1 notch will help.
Remember to Counter Steer. When you think of bike steering this way, it makes a world of difference!
This video shows it so well. Yes it works on bicycles, esp those at high speed and with large wheels or heavy tires.
Unrelated: prog metal that will blow your mind
Blotted Science - Cretaceous Chasm - YouTube
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