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I've formulated using Lagrangian formalism the equations of motion for a spinning top. I know about the gimbal lock/singularity that occurs at theta=0 and I was wondering if there was any other way to do it without dwelving into quaternions.

Yogi published a paper "A Motion of Top by Numerical Calculation" suggesting a replacement: [itex]\dot{\beta} = \dot{\varphi} cos \vartheta[/itex] and [itex]\dot{\alpha} = \dot{\varphi} sin \vartheta[/itex], but this hasn't worked for me (I find myself getting [itex]\ddot{\alpha} = 0[/itex], which isn't true)

I've had a look at quaternions but I'm not inclined to understand it or be able to simply 'convert' my equations over into quaternion calculus, neither (I believe) can I use Lagrangian mechanics on quaternions.

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# Eliminating the Euler Angle singularity without quaternions?

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