2
$\begingroup$

I'm having a hard time visualizing the gimbal lock problem. Suppose $p=(a,b,c)$ is a point where the euler angle $f:\mathbb R^3\to SO_3$ has zero jacobian determinant. Then to say that $p$ is where gimbal lock occurs can be mathematically formulated as saying that $f$ has no bijection from a small area around $p$ to a small ball around $f(p)$.

So there are rotations very close to $f(p)$ which cannot be represented as $f(p+\epsilon)$ for small $\epsilon$. I am having a hard time visualizing this. Does someone have a way to see that such rotations cannot be represented as $f(p+\epsilon)$?

  • 0
    @joriki I don't think wikipedia gives a full explanation. The image of a small ball around $p$ under $f$ does not contain a small ball around $f(p)$. A full explanation would give an explicit description of the geometry of the image of the ball around $p$ under $f$.2012-02-13

0 Answers 0