All Questions
275
questions
0
votes
0
answers
88
views
Calculating a building's shade with building height
I work in GIS and to create a shade layer of a building, I need to "translate" the geometry/building or permanenently move it.
But I just need some help with my formula based on this video.
...
- 101
1
vote
0
answers
38
views
Change orientation of turns of a trajectory
Consider a robot following the dynamical system $R_B'=R_B\exp(\omega_B^{\times}), v_W'=R_B\alpha_B + g_W$, where $R_B\in SO(3), v, \alpha, \omega, g \in \mathbb{R}^3$, and $\omega^\times$ is the skew ...
- 2,109
6
votes
2
answers
240
views
How to place optimally four electrons on a sphere?
$\newcommand{\S}{\mathbb{S}^2}$
Let $x_1,x_2,x_3,x_4 \in \mathbb{S}^2$ be points on the unit sphere, that minimizes the quantity
$$
E(x_1,x_2,x_3,x_4)=\sum_{i < j}\frac{1}{\| x_i - x_j \|},
$$
...
- 25.3k
1
vote
1
answer
58
views
Geometry: path length in atmosphere ("round" Earth)
I'm having trouble obtaining this physics formula. Since it's mostly about geometry, I hope it isn't out of place here.
I'll paste the text from the book:
Considering the curvature of the Earth (R is ...
- 13
0
votes
1
answer
34
views
Does the resultant vector stay the resultant vector after the drawing of the transversal?
Question:
Two forces of magnitude $4P$ and $3P$ acting at a point O have a resultant of magnitude $5P$. If any transversal cuts the lines of action of the forces at the points R, S, and T respectively,...
- 3,186
2
votes
2
answers
126
views
Confusion regarding volume of fluid displaced by a partially immersed body
Say I have a cylindrical apparatus partially filled with a water column, the height of the column being $h$. Now I have a solid cylinder of radius smaller than the apparatus and height $H>h$ but ...
1
vote
1
answer
68
views
How do I get the time it takes to travel between two points in a circular motion? [closed]
I have two points on a circle.
Circle with two points
Given that I have the constant angular velocity, cartesian coordinates of the two points and center, and the radius. How would I get the time it ...
- 15
0
votes
1
answer
182
views
Expressing $\phi$ and $\theta$ in terms of time difference of arrival
I have an experimental setup consisting of three receivers with known locations $\langle x_i, y_i, z_i \rangle$, and a transmitter with unknown location $\langle x,y,z \rangle$ emitting a signal at ...
- 1,381
1
vote
1
answer
171
views
Ball with diameter collision with inclined wall/plane in 2D Coordinate System
Given the position of a ball, the diameter, a direction/target position and the 4 edges of a rectangle(2:1 ratio) how can I find the end position (coordinates of a point) of a ball if it collides with ...
0
votes
1
answer
105
views
Tilting a mass suspended on 2 springs
I was trying to model the following problem:
There is a solid brick shaped body, with center of mass $(x,y,z)$. We put this body onto 2 springs. For making the problem easier, we cut out the slice ...
0
votes
1
answer
84
views
Ultrasonic anemometer: Transformation of space diagonal components to Cartesian components
We have built an ultrasonic anemometer measuring 4 components of air velocity along the 4 space diagonals of a cube. The space diagonals can be characterized by vectors (1,1,1), (1,-1,1), (-1,1,1) and ...
- 31
5
votes
3
answers
236
views
Relations Between Probability Distributions and Physical Phenomena
I have created a $3$-dimensional visualization of the Central Limit Theorem in Mathematica...
However, when flipped upside down, from below it looks suspiciously like light being emitted from a ...
- 1,922
1
vote
1
answer
314
views
Maximum horizontal force that does not cause block to slide up ramp
You are sliding a block with mass m up a ramp inclined at an angle of $\theta$ with respect to the horizontal where the coefficient of static friction between the block and the ramp is $\mu_s$. What ...
- 1,225
3
votes
0
answers
37
views
Smallest Polymer that can Pass through a Circular Orifice
In a microfluidic setting, I have encountered a puzzle of finding the minimum size (smallest total-length $L$) of a polymer (can be hyperbranched or loop, whatever shape that you can make from merging ...
- 81
6
votes
2
answers
190
views
When do two triangles reflected over midpoints have the same area?
Suppose I have a triangle ABC. I have points C', A', and B' on segments AB, BC, and CA, respectively. Suppose I reflect C' about the midpoint of AB to get point C'' (also on AB); similarly for the ...
