Timeline for How do I write the gradient in angular coordinates ($\theta_1$, $\theta_2$, $\theta_3$)?

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Feb 14, 2023 at 22:34	comment	added	Stack Exchanger		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).
Feb 11, 2023 at 20:01	comment	added	Eli		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
Feb 11, 2023 at 19:57	history	edited	Eli	CC BY-SA 4.0	added 6 characters in body
Feb 11, 2023 at 18:12	comment	added	Stack Exchanger		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 $x, y, z$?
Feb 11, 2023 at 14:48	history	edited	Eli	CC BY-SA 4.0	added 273 characters in body
Feb 11, 2023 at 14:30	history	answered	Eli	CC BY-SA 4.0