leftJacobian implementation cannot echo the formula in given PDF

[dzywater]

leftJacobian implementation cannot echo the formula in given PDF

[NikolausDemmel]

I think both are correct. Note that $\mathbf{a}$ in the report corresponds to omega / theta in the code. You can see the equivalence using the identity $\hat{\mathbf{a}}^2 = \mathbf{a} \mathbf{a}^\top - I$.

More practically, we have the same variant of the formula in Basalt and a unit test that verifies the Jacobian numerically.

It is my understanding that the version of the formula in the code, while analytically equivalent, has better numerics.

[dzywater]

I think both are correct. Note that a in the report corresponds to omega / theta in the code. You can see the equivalence using the identity a^2=aa⊤−I.

More practically, we have the same variant of the formula in Basalt and a unit test that verifies the Jacobian numerically.

It is my understanding that the version of the formula in the code, while analytically equivalent, has better numerics.

Thanks. I got it.