Reputation
3,287
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
6 28
Newest
 Revival
Impact
~158k people reached

Mar
17
comment How can I interpret $2 \times 2$ and $3 \times 3$ transformation matrices geometrically?
The above A is not an orthonormal transformation because the 1st and 3rd columns are identical.
Mar
17
comment Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
Computer Algebra System : en.wikipedia.org/wiki/Computer_algebra_system
Mar
17
comment Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
I used a CAS for speed and accuracy. I see you went one up on terms. Well $f \approx \sqrt{x} \left(r+\frac{r^3}{8}+\frac{7r^5}{128}+\frac{33 r^7}{1024}+\frac{715 r^9}{32768} \right)$ with $r=y/x$.
Mar
17
answered Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$
Mar
5
answered Calculate the radius of a circle given the chord length and height of a segment
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
Funny how math works correctly sometimes.
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
Did you read en.wikipedia.org/wiki/Tangent_half-angle_formula?
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
I added more details to the solution.
Feb
27
revised Closed-form solution for 3D rotation angles given pre- and post-image
added 416 characters in body
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
Your equation is $[A,B,C] = RY(-\varphi) RZ(-\theta) [x,y,z]$. I rearranged it and considered only the last two components
Feb
27
comment Closed-form solution for 3D rotation angles given pre- and post-image
You convert an equation with sines and cosines into a polynomial equation. It is a well known trick in robotics.
Feb
26
answered How to calculate the angle made by 3 coordinates without using cosine rule
Feb
26
comment How to calculate the angle made by 3 coordinates without using cosine rule
You mention x and z coordinates, but the picture in in the y z coordinates.
Feb
26
answered Closed-form solution for 3D rotation angles given pre- and post-image
Feb
26
comment Closed-form solution for 3D rotation angles given pre- and post-image
Can you include one sample data point so we can check the algo.
Feb
26
revised Closed-form solution for 3D rotation angles given pre- and post-image
Changed $sin$ to $\sin$. I feel better now.
Feb
22
answered Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system
Feb
20
comment What is the formal mathematical representation of a “force”?
Yes $\vec{M} = \vec{r} \times \vec{F} + \tau \vec{e}$ will produce a screw with pitch $h =\frac{\tau}{F}$
Feb
20
revised What is the formal mathematical representation of a “force”?
added 332 characters in body
Feb
20
comment What is the formal mathematical representation of a “force”?
Yes, but if you are given a $\vec{F}$, $\vec{M}$ pair you are not guaranteed that there isn't going to be a torque component parallel to the force axis. Also there aren't any nice 5 parameter sets to define this scenario. The above takes the 6 plucker coordinates of a line $(\vec{\ell}, \vec{r}\times \vec{\ell})$, treats the norm of $\vec{\ell}$ as the force magnitude.