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How to interpret the condition of a circumference rolling without slipping on another circumference

The circle with center $O$ is not moving, so the velocity of the point of contact must be zero. Let $P$ be the point on the circle with center $\Omega$ that is initially in contact with circle $O$. ...
• 100k
Accepted

Why doesn't the rotation of a inertia tensor by a rotation matrix cancel itself out?

Matrices don't generally commute. Generally speaking, $RI \neq IR$ and $IR^T \neq R^TI$ for $I$ the inertia tensor and $R$ a rotation matrix. You'd need at least one of those to be true in order to ...
• 1,413
Accepted

Rotation along Cartesian coordinates in terms of $\theta$ and $\phi$ of spherical coordinates

Visually, it it clear to make $\vec{v}$ parallel to $\hat{r}$ we should first rotate about the $\hat{z}$ axis by angle $\varphi$, then about the rotated $\hat{y}$ axis by angle $\theta$. By the ...
• 883
1 vote

Rotating a given plane into another given plane

I'm not 100% sure that I understood what the question is, but I'm sharing my thoughts anyway. As fas as I can tell you are on the right track, but I think there are snakes in your paradise. More about ...
• 135k
1 vote

Rotate multidimensional vector at a given direction with alpha

General rotations (linear transformations preserving length and orientation) in higher dimensions get tricky: In 2 dimensions, a rotation is completely determined by an angle. In 3 dimensions, a ...
• 7,714

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