Skip to main content
Physics

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

3
  • $\begingroup$ Thanks! So in this case, $\nabla$ is the Jacobian times a row vector of the $\theta_1, \theta_2, \theta_3$ (or $\psi, \theta, \phi$), with the Jacobian being the matrix that transforms $\theta_1, \theta_2, \theta_3$ to $x, y, z$? $\endgroup$
    – Stack Exchanger
    Commented Feb 11, 2023 at 18:12
  • $\begingroup$ The Jacobian Matrix is $~J_{i,j}=\frac{\partial P_i}{\partial \b q_j}~$ partial derivative of the position vector to the generalized coordinates. Try to obtain the Nabla vector for the sphere with this concept ! I did_'t used $~\theta_i~$ instead I used $~\psi~,\theta~,\phi~$ yaw pitch ans roll angle $\endgroup$
    – Eli
    Commented Feb 11, 2023 at 20:01
  • $\begingroup$ Thanks. Using this concept,to go from $(\theta_1, \theta_2, \theta_3)$ to $(x, y)$, I got the Jacobian $J = (\sum_i \frac{\partial^2 x}{\partial \theta_i^2} \sum_i \frac{\partial^2 y}{\partial \theta_i^2})^{T}$. The follow up question I had from this is how to express $x$ and $y$ in terms of these three angles (spherical coordinates just has two). The physical problem I am working with is planar, so there is no $z$ axis, but still these three angles (all three are not fully independent of each other). $\endgroup$
    – Stack Exchanger
    Commented Feb 14, 2023 at 22:34