Questions tagged [geometry]

To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

98 questions with no upvoted or accepted answers
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335 views

The dual of a surface element in 4-space

In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the ...
5
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2answers
396 views

Combining rotations for orbital and rotational motion of a planet

If I have a planet orbiting the Sun (assuming circular orbit) at angular velocity $\Omega$ and rotating about its axis at $\omega$. I also have a normal to the surface of the planet $\vec{n}_{\rm surf}...
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1answer
216 views

(I-beam vs rectangular beam) Which sword blade cross section is less likely to break?

Original question Assumption: i made several swords with different cross sections (lenticular, single broad fuller as in viking swords, diamond, hollow ground diamond) the blades are made using the ...
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0answers
269 views

Snyder's Lorentz invariant discrete space-time

Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous? I'm sure this has been ...
4
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2answers
183 views

When is a circle not a circle?

Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle. Now imagine the same ...
4
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3answers
775 views

Finding the illuminance from a triangular light source

Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light ...
3
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0answers
36 views

Looking for a geometric cosmology model where time behaves like an orientation

This question is literally inspired from seeing the above scene unfold. Let the merging and splitting light spots you saw in the above gif be pairs of particles and anti particles, let the shape of ...
3
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0answers
70 views

What are the relations between a ladder algebra and an $SU(2)$ algebra?

I am studying elementary models of the Quantum Hall Effect. I don't have a strong background in Lie algebras so I was hoping someone could elaborate on the following observation: For a free particle ...
3
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1answer
215 views

New way to compensate for gyroscopic drift

Let us assume two points in 3D space and we only care about their orientation, no velocity, position or acceleration. Now connect those two points with a rigid body of certain length, so that the ...
3
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0answers
128 views

What is the geometric explanation for why the interior angles of a triangle sum to 180 degrees in both Euclidean space and Minkowski spacetime?

Four-dimensional Euclidean space has the same topology and affine structure as Minkowski spacetime, though the two have different metric structures. Given that the interior angles of a triangle ...
3
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0answers
80 views

Rigid rectangle in Schwarzschild

Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial ...
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0answers
1k views

Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
2
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1answer
82 views

Why did staining marks on these paving slabs form geometric shapes?

[edited to add more examples] Along several streets in London I can see paving slabs that have become stained in the middle of the slab with white-ish marks forming different shaped patterns. The ...
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0answers
29 views

What should be the shape of an axisymmetric solar reflector that provides a uniform flux on the surface of a circular cylinder placed on its axis?

I was wondering about creating a solar concentrator with an antisymmetric concave shape that is able to focus the collected light onto a circular cylinder positioned on the concentrator axis. The ...
2
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0answers
53 views

How to interpret Einstein's development of Euclidean orthogonal transformations in The Meaning of Relativity?

My questions pertain to the development of Euclidean 3-space orthogonal transformations presented in Einstein's The Meaning of Relativity. Also available at https://en.wikisource.org/wiki/...
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136 views

Spinors in Classical Mechanics and Geometry?

I'm trying to deepen my understanding of spinors by looking at applications in simple problems, preferably unrelated to quantum mechanics. For this purpose I'd like to refrain from discussing ...
2
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0answers
112 views

What would gravity be like on the surface of a right rectangular prism?

Let's assume there is a right rectangular prism floating about in space, what would the gravity be like across its 6 flat surfaces? Let's assume that this right rectangular prism has a constant ...
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0answers
252 views

What is the connection between the Foucault pendulum and parallel transport?

I try to explain the Foucault pendulum with the concept of parallel transport(if we think of Earth as being a perfect sphere) but I can't quite figure out what the vector that gets parallel ...
2
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0answers
60 views

Examples of multiply-connected compact configuration spaces

I'm a looking for examples of dynamical systems that have multiply-connected compact configuration spaces. Since I'm not a 100% sure about the correct terminology for the systems (I am sure about the ...
2
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1answer
68 views

Satellite and gravitational acceleration

According to $0.5gt^2$ object will fall 5m in first second. Earth curve is 5m for 8km So if we can project object at 8000 m/s speed object will never fall into ground. Above scenario is correct for ...
2
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1answer
284 views

Center of mass/centroid changes between 2D and 3D?

Unless I completely botched the calculation, I noticed something strange: if you find the centroid of a 2d curve, and then revolve the curve around its axis then find the center of mass, the CM is ...
2
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0answers
74 views

Terminology - optical (visual) properties of a structure

I am trying to understand few terminological problems that I encounter. Without knowing keywords it is hard to perform search for literature or publications in the area. The area relates to the ...
2
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0answers
393 views

Circumference measurement using a capacitive sensor

I have a question which I hope someone in here can help me answer. Background: I’m building a device where I intend to use a stretchable capacitive sensor to define the radius change of an object. ...
2
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0answers
110 views

Is there a theory that physically explains the origin equivalence principle / explains gravity via acceleration?

I've been thinking about how gravity could arise from a 4th dimensional spinning cylinder with space-time that has pliability like rubber (which I think is a generally accepted analogy). The ...
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0answers
93 views

T duality for lower codimension branes or ALF spaces

These are purely mathematical questions in some sense but I believe this is relevant in string theory as the title says. I wonder if it is possible to perform T-duality of Taub-NUT space not along ...
2
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0answers
411 views

Can we derive the relation between proper time and the spacetime interval?

In GR, it's usually taken for granted - or as a definition - that the time measured by an observer's clock is related to the geometry in a very simple way, $d\tau^2 = |ds^2|$. This is easy enough to ...
2
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1answer
346 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
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0answers
99 views

Dirichlet's work on gravity in non-Euclidean space?

In the book The Norton History of Astronomy and Cosmology by the late John North I have found the following statement (page 514): "The German mathematician Lejeune Dirichlet studied the law of ...
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251 views

Getting the AdS metric from maximally symmetric spaces

I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. ...
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0answers
118 views

Does the measure of proximity of two theories in “theory space” run?

From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the ...
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105 views

Self-organizing maps

I'm currently interested in this subject but all I can see is about neural networks and I'm more interested on the Theoretical point of view: "how can a system (Lagrangian/Hamiltonian) alter it's ...
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28 views

What is meant by “neighboring points”?

I have recently been frequently encountering the phrase "neighboring points" during my studies. For example: Fermat's Principle. Optical rays travelling between two points, $A$ and $B$, follow a ...
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1answer
49 views

Theoretical question regarding two elliptic trajectories

I am new to Newtonian Mechanics, and I was wondering regarding the following: Are $$\vec{r}(t): a \sin(ωt)\hat x +b\cos(ωt)\hat y$$ and $$\vec{r}(t): a \sin(ωt^2)\hat x +b\cos(ωt^2)\hat y$$ ...
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23 views

Consistency with calculating the Solar Azimuth Angle

I am struggling to find consistency regarding the calculation of the Solar Azimuth Angle. The equations across multiple publications have similar terms, but differ significantly. These differences ...
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0answers
27 views

Geometrical way to view discretization of energy in quantum mechanics. How commutation relation implies discreteness?

The relation from which discreteness in eigenvalue of the energy of bound state arises is $[x, p]=i\hbar$ followed by the rule that wavefunction should be normalizable. So my question is there a ...
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1answer
196 views

What is the diameter size of the umbra shadow cone of the Earth when the Moon passes through it on a lunar eclipse?

I am sure this varies given the distance from moon to earth varies, but a range would be sufficient. I am trying to explain to a flat earther how there is not a lunar eclipse every full moon. My ...
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0answers
61 views

Electric Potential Energy in $0$ space like dimensions and $t$ time like dimensions in the case of massive photons

Several months ago I asked about electric force in higher dimensions in the case of massive photons What would be the force law for the electric force between two electric charges in higher dimensions ...
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274 views

Calculating the Gaussian Curvature of Cylinder

In the book "Gravitation" by Misner, Thorne and Wheeler, exercise 1.1 on page 44 reads: Show that the Gaussian curvature $R$ of the surface of a cylinder is zero by showing that geodesics on that ...
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1answer
69 views

Doubt in the equation of trajectory of partical moving under central Force

In the book by Goldstein (Third Edition, Page 95) on classical mechanics, Goldstein derives equation of the trajectory of particle moving under center force. The equation he derives is given by: $$r= ...
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27 views

Attitude quaternion from 2 vector measurements

I am using a method proposed by R. G. Reynolds to estimate attitude based on two vector measurements, taken from: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990052720.pdf Suppose we ...
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0answers
71 views

How to “picture” a principal Poincare-bundle?

Let $(P,\pi,M)$ be a principal $ISO(1,3)$-bundle. I suppose that in local trivialisation, the total space should look like $M\times ISO(1,3)$, since the fibre is isomorphic to the structure group. It ...
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39 views

What coordinate system produces this particular form of the line element of de Sitter spacetime?

To save space, all the symbols and conventions are adopted from this Wikipedia article. We know that the line element of $n$ dimensional de Sitter space in static coordinates is $$ds^2=-\bigg(1-\...
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1answer
206 views

Deformation of a self gravitating sphere from two forces

I have a fluid sphere (say a gas or a liquid of uniform density, under its own gravity) on which forces is applied to its surface. I would like to find its approximate shape (most probably an oblate ...
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69 views

Orbifolds for non-conformal theories

By now, a lot is known about orbifolds of 1+1-dimensional CFTs. Consider starting out with an arbitrary 'seed' CFT, $\mathcal{C}$, and take $N$ copies, $\mathcal{C}^{\otimes N}$ and then quotient by ...
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63 views

How is it possible to see Surfer's Paradise from Coolangatta?

I've came across some photos in the internet, which were taken at Coolangatta. In this photos, it's possible to see the buildings from Surfer's Paradise(both of these places are located in Australia). ...
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0answers
82 views

Is there a 3D analogue of angle?

A one-dimensional angle is a wedge, almost like a slice of pizza. A two-dimensional angle is an angle squared, like the cone of light produced by a flashlight. This is called a solid angle. Is ...
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0answers
28 views

What determines the sign of phase dislocations?

I am studying the nonlinear Schrodinger equation $$A_t+iA_{xx}+i|A|^2A=0$$ for $A=ae^{i\theta}$ a complex valued function, with $a,\theta$ real. I am trying to figure out what sets the signs of the ...
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0answers
267 views

Does Earth eclipse the Sun at the L2 Lagrange point?

Is Earth's diameter large enough to eclipse the sun at the L2 Lagrange point? Or does the sun shine around the edges of the earth? I understand the useful area of the L2 Lagrange point is somewhat ...
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0answers
97 views

Derived Geometry and Deformation Quantization

Can anyone please explain to me in layman' terms what derived geometry deals with and what deformation Quantization is? I have only a good understanding of Relativity,Classical Mechanics.
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59 views

Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...