29 lines
1.1 KiB
Markdown
29 lines
1.1 KiB
Markdown
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title = "Angular Velocity"
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author = ["Thomas Dehaeze"]
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draft = false
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## Non-integrability of the angular velocity vector {#non-integrability-of-the-angular-velocity-vector}
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The non-integrability of the angular velocity vector is well described in ([Legnani et al. 2012](#orga01afc4)).
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> It is well known that the angular velocity vector is not the time derivative of any set of angular coordinates.
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> In other words, it is impossible to define a set of three coordinates representing the 3D angular position of a body whose time derivative is equal to the angular velocity vector.
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This is illustrated in Figure [1](#org4ad23f3).
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<a id="org4ad23f3"></a>
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{{< figure src="/ox-hugo/angular_nonintegrability.png" caption="Figure 1: Effect of different sequences of rotations of a rigid body. In both cases we get Rot(x)=0, Rot(y)=90deg and Rot(z)=90deg" >}}
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## Bibliography {#bibliography}
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<a id="orga01afc4"></a>Legnani, G., I. Fassi, H. Giberti, S. Cinquemani, and D. Tosi. 2012. “A New Isotropic and Decoupled 6-Dof Parallel Manipulator.” _Mechanism and Machine Theory_ 58 (nil):64–81. <https://doi.org/10.1016/j.mechmachtheory.2012.07.008>.
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