All Questions
24
questions
2
votes
1
answer
104
views
Calculating deflection on a beam
This is for a hobby project, and to learn a little about elasticity along the way.
I have a triangle wedge comb piece of decreasing width and angle for which the cross section is shown here:
For each ...
- 406
4
votes
1
answer
70
views
Modeling Nanotubes Geometry
In various references, we see the construction of unit cells of carbon nanotubes (CNTs) from chiral and translational vectors.
The chiral vector is given as:
$$\vec C_h = n\vec a_1 + m\vec a_2$$
...
- 3,789
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
0
votes
1
answer
58
views
What is the meaning of this formula (y2-y1) * cos ((x1+x2) /2)? [closed]
Can anyone please explain the meaning of the cos((y1+y2)/2) in this formula please?
Note: the constant 6371 is the earth's radius
- 101
5
votes
1
answer
1k
views
Eccentricity Vector of an Ellipse -- Geometric Derivation?
I've been playing Kerbal Space Program again, and so I'm learning about orbital mechanics. There's a particular vector I can derive physically, but it's an intrinsically geometric object, and so I'd ...
- 13.1k
3
votes
2
answers
1k
views
Is Minkowski space a Hilbert space?
In other words, is Minkowski space a real or complex inner product space that is also a complete metric space with respect to the distance function induced by the inner product? I would think that ...
- 31
0
votes
2
answers
505
views
Ground Vehicle Handling: Is it possible to calculate the speed at which to take a turn given a turn angle and a vehicles current speed?
I'm working on AI vehicle movement for a game. This is an open terrain game so the vehicles are not using a predefined track. The AI is given a list of waypoints that they must follow believably. ...
- 3
11
votes
1
answer
397
views
What would you see inside a spherical mirror?
Image to build a huge spherical shell made of semitransparent glass, and to cover the internal part with a reflecting material.
In such structure some light can enter, and an observer inside it (e....
user559615
3
votes
2
answers
739
views
Prove for the time derivative of a vector with constant magnitude
First of all, sorry for my bad English, I have several doubts about the geometric demonstration made by Kleppner for the derivative of a vector that has a constant magnitude, page 25, which is ...
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
2
votes
0
answers
92
views
Criteria of a manifold
I am self studying Frankel's The Geometry of Physics, early in the text he poses the example:
The x axis of the xy plane can be described as the locus of the quadratic $F(x,y) := y^2=0$. Both ...
- 111
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
2
votes
0
answers
45
views
Calculating the coordinates on a given space that produce a desired form of the metric.
Consider the case of the 4-dimensional de Sitter space, $dS_4$:
the hyperboloid given by $$-x_0^2+x_1^2+x_2^2+x_3^2+x_4^2=\alpha^2,$$
embedded in in 5-dimensional Minkowski spacetime, $R^{1,4}$, ...
- 493
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 ...
