Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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2
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1answer
166 views

Associativity of Moyal-like products

The Moyal product of two smooth functions $f,g$ on $\mathbb R^{2n}$ can be defined as $$ f\star g = \exp\left(-\omega^{ij} \frac{\partial}{\partial y^i} \frac{\partial}{\partial z^j}\right) f(y)g(z) ...
0
votes
2answers
143 views

How to calculate the resulting velocitys and rotation speed after two concave polygons collide in 2d

so I've been searching google for how to do this, but all anyone seems to care about is collision detection =p, and no results come close to teaching me how to calculate 2d elastic collision between ...
1
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2answers
2k views

2D elastic collision equation: How does it work?

Hey so I recently started learning physics, and came upon this wonderful site that taught me how to calculate 2D collisions between two circles. The only part I'm confused about is how the velocity ...
12
votes
4answers
1k views

Pure maths vs applied

Is there any point in an aspiring theoretical physicist doing pure math topics such as analysis? (Assuming that he would not be doing them out of pure interest.)
1
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1answer
126 views

Help with volume integration

I need help solving this integral ($\hat{z}$ denotes the polar axis):$$\int_V\dfrac{\vec{r}\cdot(\vec{r}-c\hat{z})}{|\vec{r}|^3|\vec{r}-c\hat{z}|^3} dV$$ Where $V$ denotes all space. Attempt: $$2\pi ...
1
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0answers
83 views

Does triality survive in product Lie groups?

Look at the following diagrams of Lie groups ...
3
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2answers
870 views

Hankel function in terms of planewaves

It is well know that planewaves are a complete basis for solutions to the wave equation. Let us assume a 2D space, and at fixed temporal frequency, the equation reduces to the Helmholtz equation. In ...
1
vote
3answers
172 views

What is the gravitational force imposed by a rectilinear 2d body?

I'm starting with the simplest problem I can relate to mine: the force imposed on a point mass at the origin by a rectangle that is orthogonal to the $x$- and $y$-axis, stretching from $(x_1, y_1)$ to ...
1
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1answer
2k views

Calculating time taken to get down a slope

I'm doing my homework for a Physics class and trying to get ready for a quiz. I encountered this question: Two ramps of equal length are situated such that ramp #1 has a slope (with respect to ...
-1
votes
1answer
6k views

Pascals to PSI formula [closed]

Could somebody give me a formula to convert Pascals to PSI? I understand that you probably have to convert Pounds of Force to Newtons. But where do I go from there?
3
votes
3answers
117 views

Distance and time

So basically I have a said distance. There is one object moving at said speed from one side to the other(lets call it A to B), and another object moving at a different speed(faster speed) from the ...
5
votes
3answers
460 views

Physics: Uniform Motion

Ok so I have this homework problem. I dont want to give out the information because i want to put in the values myself, but basically I have one object moving at said speed. Said time later, another ...
2
votes
2answers
432 views

Transforming a sum in an integral

I have a second question about the article "Imperfect Bose Gas with Hard-Sphere Interaction". The authors begins with the sum: $$\frac{{E_2 }}{{E_0 }} = \frac{{16\pi ^2 a^2 \lambda ^2 }}{{V^2 ...
1
vote
1answer
916 views

What is this question asking about vector components?

Here's a question from my homework: Two vectors are given by a = 1.9i + 3.2j and b = 1.6i + 8.6j. Find (a)|a × b|, (b)a · b, (c)(a + b) · b, and (d) the component of a along the direction of ...
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0answers
86 views

Partial differential fields and logic

Is the theory of partial differential fields a first-order or higher-order logic theory? Is the theory of differential fields already equipped with partial derivatives? I was told that the General ...
0
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2answers
3k views

How to solve this problem using Calculus?

During a homework problem I was supposed to solve this using Calculus. Here's the problem: A cow car is traveling at $50 \ \text{mi}/\text{h}$ when the brakes are fully applied, producing a ...
2
votes
2answers
894 views

Basic free fall

It takes 0.210 seconds for a dropped object to pass a window that is 1.35 meters tall. From what height above the top of the window was the object released? Air resistance is negligible. I get 1.5 ...
3
votes
3answers
557 views

Basic kinematics question

Starting from rest a lady bug runs along a straight line with constant acceleration. After time T1 , the lady bug suddenly reverses the direction of its acceleration but keeps the magnitude of the ...
2
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1answer
406 views

Illustration of vector calculus vs. differential forms

I am looking for a nice illustration of how vector calculus relates to differential forms. A demonstration that employs physics is appreciable (e.g. electromagnetism). In particular, while dualizing ...
6
votes
3answers
2k views

What is a physical “dimension” - in the sense of “dimensional” analysis?

Mathematically speaking, what does it mean to say that a physical quantity is some numerical value with a “dimension” associated with it? When we say that the velocity of light is some constant, c ...
3
votes
1answer
1k views

Please help me understand vectors

I'm about to cry. I can't get this and it's frustrating beyond belief. Here's a problem in my homework: Oasis B is a distance d = 9 km east of oasis A, along the x axis shown in the Figure. A ...
2
votes
2answers
118 views

How to set up this vector problem?

Reading through my homework, I encountered this. I don't know what a picture of this would look like, and how to decompose into separate vectors. Once I figure out what I need to decompose into, I ...
3
votes
0answers
180 views

What can we say about $n\times n$ invertible matrices, all elements of which are $+1$, $-1$, or $0$?

Basically, the title says it all, except for why I am asking. I'm studying a paper that I can't do justice to in a few words here. (It is not freely available on the Web, as far as I know, but I can ...
0
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1answer
2k views

How to make simple iteration in Mathematica

How to make simple iteration in Mathematica for this three equations and save $q$ for each step. If we define $q'=dq/dx$, $q''=dq'/dx$ we have two equations (1) ...
2
votes
2answers
270 views

What does $\mathrm{ms}^{-1}$ mean?

A baseball is hit with a velocity of $28.0 \ \mathrm{ms}^{-1}$. Should I just ignore this, or is it actually part of the question, what does it mean?
1
vote
2answers
353 views

Physics Question about parabola projectile angle

A projectile is launched over level ground at $35 \frac{m}{s}$ at an angle of $24^{\circ}$ above the horizontal. Friction is negligible. What is the velocity (magnitude and direction) of this ...
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2answers
1k views

Quadratic formula with negative square root?

I encountered this while doing a very basic physics question (so I hope you don't mind if I post it, the problem lies within my math anyways): A stunt vehicle leaves an inclined slope of 28 degrees ...
2
votes
3answers
395 views

Move two wheeled robot from one point to another

The inner circle represents the potential path of the left wheel, and the outer the potential path of the right. The circle in between represents the "midpoint" between these two circles. Given ...
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0answers
556 views

How to make iteration for Newmark method in Mathematica 8

How to make iteration method for solving differential equations by Newmark method? There are just three equations which describe the Newmark method. I need q for time step for example 0.01. Also, for ...
3
votes
1answer
160 views

Simulation of bouncing circles

I want to simulate two circles bouncing off one another. For this I am not sure what I need to calculate. I couldn't find any useful information on the internet, so I have thought long and hard about ...
2
votes
1answer
225 views

Embrace applied mathematics [closed]

Does anyone have any suggestions as to what is a good topic for a short talk on theoretical physics to a bunch of Math and Physics undergrads that might make them "embrace" theoretical physics? ...
3
votes
1answer
280 views

dynamic mean: measurement of randomly distributed events

Aim is to estimate an error on a stochastic event rate. I read out the event counter second-wise, every black $1$ is a counted event (new events over time, see the plot below). During the measurement ...
2
votes
2answers
431 views

It is physically intuitive that the catenary is unique?

The catenary minimizes the potential energy of a cable and has equation $y - y_0 = A \cosh (\frac{x-x_0}{A})$. It is physically intuitive that the catenary is unique, but is there a mathematical ...
8
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3answers
2k views

Property of Dirac delta function in $\mathbb{R}^n$

How does one prove the following identity? $$\int _Vf(\pmb{r})\delta (g(\pmb{r}))d\pmb{r}=\int _S\frac{f(\pmb{r})}{|\text{grad} g(\pmb{r})|}d\sigma$$ where $S$ is the surface inside $V$ where ...
3
votes
2answers
434 views

Uniform Load on an Elastic Bar

One applied math question talks about an elastic bar with a displacement equation $du^2/dx^2 = 1$ for a uniform load and fixed on both ends. I solved this using the Toeplitz matrix K and u comes out ...
5
votes
4answers
657 views

Numerical computation of the Rayleigh-Lamb curves

The Rayleigh-Lamb equations: $$\frac{\tan (pd)}{\tan (qd)}=-\left[\frac{4k^2pq}{\left(k^2-q^2\right)^2}\right]^{\pm 1}$$ (two equations, one with the +1 exponent and the other with the -1 exponent) ...
3
votes
2answers
416 views

boundary defining functions

Suppose that $M$ is the interior of a compact manifold with boundary $\partial M$. I'm often faced with so called boundary defining functions - or just 'defining functions'. That are by definition ...
1
vote
1answer
114 views

Optimal method to numerically integrate a spectral distribution data

I am trying to numerically integrate a spectral distribution data. A spectral distribution function gives the Luminosity per Wavelength of an object (like a galaxy) as a function of the Wavelength. In ...
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0answers
190 views

Computation of Clebsch-Gordan cofficients for point groups

In my work I have to deal with space and point groups and their representation. A lot of computations need Clebsch-Gordan coefficients. I am aware of the fact that these coefficients may be found in ...
1
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4answers
8k views

Converting a function for “velocity vs. position”, $v(x)$, to “position vs. time”, $p(t)$

Provided some initial point $x(0)$, how do I convert the function for velocity vs. position, $v(x)$, into a function for position vs. time, $x(t)$, with time derivative $v(x(t))$? Constant ...
0
votes
1answer
9k views

how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude?

Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. OK here's the problem: I am given a three dimensional velocity vector (I know the ...
0
votes
1answer
122 views

Simple physics for a graphical user interface widget

I have developed a spinner view for an Android application. It's like the spinner wheel on the Price Is Right with Bob Barker (If you're not familiar with that show watch this video). I am looking ...
5
votes
1answer
249 views

Dyson series and T product (II)

After reading the previous posts related to the Dyson series, I have decided to open a new thread because there is something that I am still not understanding. It concerns the expression: $$ ...
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vote
4answers
811 views

How to solve for an unknown in two different denominators?

How to solve for an unknown in two different denominators? In this equation: $$F = \frac{GMm_3}{r_2} - \frac{Gmm_3}{d-r_2}.$$ Everything is given except for $r_2$. How do I solve for $r_2$? Is it ...
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vote
2answers
2k views

Determining the peak speed of an accelerating/decelerating body between two point

A point moves from point A to point B. Both points are known, and so is the distance between them. It starts with a known speed of VA, accelerate (with known constant acceleration a) reaching VX ...
2
votes
1answer
81 views

Growth of Radially Symmetric Potential Fields

Suppose I have a function $F: R^3 \to R^3$ which satisfies: 1) There exists $\Psi: R^3 \to R$ such that $F = \nabla \Psi$ and 2) $F(x)$ depends only on $\|x\|$ Can I conclude that $\|F(x)\| = ...
2
votes
2answers
656 views

A ball is thrown, where does it bounce?

Firstly sorry if this has been asked before. I'm trying to work out a simple graphical equation that'll give me the x of the bounce point when y=0 (as it's hit the ground). I'm only after the first ...
4
votes
1answer
312 views

Fourier (Hankel?) transform of a discrete set of radial points (question from a chemist!)

I'm sorry because I'm not a mathematician so that my question may look a little bit messy. I have tabulated values [1] of a 3 dimensional radial function $f(r)$: ...
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0answers
242 views

Designing a mathematical physics class

Surprisingly, the university (a major tech school) I attended does not offer a mathematical physics class. Consequently, I often get asked by my physics friends what are some good math classes to take ...
2
votes
2answers
1k views

How to configure an LED to emit white light of a certain color temperature?

I'm working on an open source hardware project for a video/photo light, and it involves a fair bit of color math. I am trying to find my way from Color Temperature (CT) in Kelvin to current values ...