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## Main Question or Discussion Point

Hello everyone,

I need some information with angular velocity in 3D and since I'm a math student, it's been a long time I haven't worked with physics, especially mechanics. This is why I need your help.

Let's say I have this billiard ball (it's just an example) and I hit the ball with a cue with a certain angle so the ball with start rolling on the table, with a specific curve. Let's say that I know the initial angular velocity [tex]\omega(0)[/tex]. I'd like to know the ball's angular velocity at time [tex]t[/tex] with some equation using quaternions. After that, I think I'll be able to do what I want : integrate to get the angular displacement at time [tex]t[/tex].

Also, let [tex]f[/tex] be the known friction force. It's constant.

Thanks for your help and sorry for my bad English, I'm French.

If something isn't clear enough, just tell me and I'll try to give you the missing information.

EDIT : I forgot to say that the ball radius is [tex]R[/tex] and the inertia tensor is [tex]I = \frac{2\cdot m\cdot R^2}{5}[/tex] with [tex]m[/tex] the mass of the ball

I need some information with angular velocity in 3D and since I'm a math student, it's been a long time I haven't worked with physics, especially mechanics. This is why I need your help.

Let's say I have this billiard ball (it's just an example) and I hit the ball with a cue with a certain angle so the ball with start rolling on the table, with a specific curve. Let's say that I know the initial angular velocity [tex]\omega(0)[/tex]. I'd like to know the ball's angular velocity at time [tex]t[/tex] with some equation using quaternions. After that, I think I'll be able to do what I want : integrate to get the angular displacement at time [tex]t[/tex].

Also, let [tex]f[/tex] be the known friction force. It's constant.

Thanks for your help and sorry for my bad English, I'm French.

If something isn't clear enough, just tell me and I'll try to give you the missing information.

EDIT : I forgot to say that the ball radius is [tex]R[/tex] and the inertia tensor is [tex]I = \frac{2\cdot m\cdot R^2}{5}[/tex] with [tex]m[/tex] the mass of the ball

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