Flight of boomerang

Ideas
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A boomerang is a thrown tool, typically constructed as a flat aero foil, that is designed to spin about an axis perpendicular to the direction of its flight. A returning boomerang is designed to return to the thrower. It is well known as a weapon used by Indigenous Australians for hunting.

boo.jpg
boo.jpg282×288 58 KB

The code with NDSolveValue is attached.

Simulation filght of boomerang.

Anim.gif

References : “Principles and Simulation of the Flight of a Straight Boomerang” by : Nicolas Retrepo, Advisor : Dr.P.Venkataraman

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[GiF] Flight of Badminton Shuttlecocks
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Your contributions are impressive, Mariusz! You must be an expert in dynamics and well informed about the rotational motion of all sorts of objects!
This brings me to a demonstration I am hopelessly trying to get right. About the rolling of a marble inside a bowl.
Attached is a demonstration I made some time ago. I know it dies not look right and the rotations of the marble are not consistent with experience. Maybe you can have look at it or get me on the right track. Or maybe yo know a publication that has the correct equations of motion?

marble.gif

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The solution to this problem was not so hard .The required knowledge can be found on the Internet but In this case I myself solved.

You could say that your equation with a good approximation is correct . Details in the file. And then there’s one thing I’m not an expert . Only an engineer.

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Thank you, Mariusz, keep the good posts coming!

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To response see above.

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Hello,

I am new to Mathematica and was going through a few simulations and animations, and trying a few things like Rotations and Transformations.

I had one doubt, is there any way to rotate the bowl along a certain axis while the marble is moving inside it at the same time?

Will a Rotate function like below used inside Initialization work?

Rot[\[Alpha]_] := {{Cos[\[Alpha]], -Sin[\[Alpha]]}, {Sin[\[Alpha]], 
     Cos[\[Alpha]]}}
   Rot1 = bowl
   Animate[
    Graphics[GeometricTransformation[Rot1, Rot[\[Alpha]]], 
     Axes -> True], {\[Alpha], 0, 2 \[Pi]}]

Thanks

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Yes it is possible, but its more complicated. I’m not a physicist. My skills in Mathematica are average.

If you want an answers, then write a new post(discussion).