All Questions
30
questions
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
1
vote
1
answer
83
views
Find an angle to accelerate at to most quickly go from one movement vector to another
Okay, so this is with respect to game design, so that’s where I’m coming from (please try to use smol words, I am no mathematician)
I have a 2D space ship. Its velocity is defined by vector A, let’s ...
- 165
2
votes
1
answer
132
views
If I know the average value over a radial cross section, can I compute the average value over a disk (assuming radial symmetry)?
Let's say that I am trying to calculate the average velocity of a fluid through a pipe and I only know the average velocity of a cross-section through the center, can I find the average velocity in ...
- 300
0
votes
1
answer
42
views
Find 3D coordinate on same plane as given 3 coordinates
I have 4 coordinates on a plane and coordinates $A,B,C$ are known. Line $AB$ is 90 degrees to line $AD$. The distance between $A$ to $D$ is 3 meters. I am trying to find coordinate $D$.
The ...
- 5
15
votes
5
answers
6k
views
Help to identify every equation in this meme? [closed]
A couple of the equations in this meme aren’t easy to read, and I probably don’t know them so I couldn’t tell what they are.
Can you identify all the equations, and help me feel smart on twitter?
- 839
4
votes
1
answer
122
views
Is there a 3D shape with a flat face throughout which one would experience constant "downward" acceleration?
A spaceman restricted to the center of his platform
A person standing on a thin disk in space will experience gravitational acceleration exactly normal to the surface only when he is situated exactly ...
- 41
3
votes
2
answers
596
views
Ball rolling along a see-saw
Suppose we have a see-saw which is 2 metres long, whose mid-point is connected to a fulcrum which is 0.5 metres tall. The see-saw has a mass of 1kg, and has uniform thickness and density. The see-saw ...
- 1,753
2
votes
1
answer
91
views
Projected mean (p)-distance from a point to the surface of an (n)-sphere
I am considering a point R inside an sphere of radius 1 in dimension d. The point is at a distance x from the center of the sphere, and the axis 0x is thus defined.
The distance between the point ...
- 31
1
vote
3
answers
170
views
Calculus problem with right triangles
In a soccer field ABCD a player kicks the ball from a point P towards the goalpost situated on AB. The ball rolls on the ground without rising. The trajectory of the ball is parallel to AD and it's 40 ...
2
votes
1
answer
146
views
What would be the calculations behind the skyscraper view of a sunset as a demonstration of a rotating earth?
This is my first post here. I have been challenged to proved proof that the earth is not flat and that we live on a spinning ball. This was a fairly easy task for me and I proved several observable ...
- 121
0
votes
1
answer
107
views
Water resting in a sin curve
Imagine the sin function as it dips under the $x$ axis and let that part of the curve be filled with (2-dimensional) "water" up to the axis.
We can find the amount of water that fills this area by
$$...
- 3,557
0
votes
1
answer
765
views
Find hypotenuse of a sphere given radius.
Say I have a circle of radius 6 ft. How do I know that my hypotenuse is also 6ft?
It makes sense to me that from a point of origin $(0,0)$ on the circle, the x-axis and y-axis both stop at $6$ft.
...
- 575
0
votes
0
answers
34
views
Light Transport Artifacts with Signed Distance Functions
I've been messing around with ray-marched geometry for a game engine and recently messed around with a fully ray-driven lighting system. At one stage I had a very nice system that accurately traced ...
- 103
0
votes
1
answer
1k
views
A question on the solution for the lifeguard problem (or Snell's law)
This question is about the lifeguard problem as presented on the linked assignment, essentially this is related to Snell's law. In the solution, after introducing appropriate names, the condition
$$
\...
- 18.2k
0
votes
2
answers
849
views
Finding the x and y components of a vector that is projected tangent to a circle
Here is a diagram I made for the problem.
There is a very similar question on this website, but there wasn't a clear solution for that one when it came to the components of the vector. They seemed ...
