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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1answer
32 views

Calculate launch angle of projectile

I'm creating a game and am having trouble designing aiming system for AI. How do I calculate all angles at which the projectile can be launched from point $T_0(x_0,y_0)$ with launch velocity $v_0$ to ...
0
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0answers
26 views

Ternary balance with unknown weight

Main references: Ternary (Wolfram MathWorld) Balanced ternary (Wikipedia) Weighing scale: Balance (Wikipedia) <quote> Balanced ternary has other applications besides computing. For example, a ...
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1answer
51 views

I need some help understanding the tensor algebra done this problem.

I often see equations rearranged across an equal sign and I have no clue what tricks and reasoning they are using to arrive at these solutions. The only resources I can find on tensor algebra only ...
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3answers
143 views

Explanation of line element formula $dl^2 = dx^2 + dy^2$

I found this in a physics textbook without justification: $$dl^2 = dx^2 +dy^2,$$ where I presume that $l = \sqrt{x^2+y^2}$. Why is this so? By my calculations I obtain $$ dl = \dfrac{\partial ...
4
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1answer
46 views

What exactly are the curves that are a best fit to the Harmonic Cantilever?

Let's start with a few references to get an idea: Daniel Goldwater: Harmonic Cantilever Book Stacking Problem Block-stacking problem Harmonic Series and Bricks Interesting related issues: Maximum ...
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15answers
6k views

Why learn to solve differential equations when computers can do it?

I'm getting started learning engineering math. I'm really interested in physics especially quantum mechanics, and I'm coming from a strong CS background. One question is haunting me. Why do I need ...
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1answer
24 views

Setting Up an Integral (depends on displacement vector from a long line)

The following is a physics problem, but I don't actually care about the physics right now. I just want to set up the integral, which I'm having a difficult time doing (the problem is from the book ...
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1answer
36 views

The motion of the particle satisfies $\textbf{v} = \textbf{c}\times \textbf{r}$

Why is the path is contained in a circle that lies in a plane perpendicular to $\textbf{c}$ with centre on a line through the origin in the direction of $\textbf{c}$
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1answer
105 views

Why do objects that are farther away look smaller?

What is the reason, mathematical and/or physical, that the further away something is the smaller it looks? We know stars are humungous, but they look like tiny dots in the sky.
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2answers
48 views

Constants for anti-derivatives

Hey StackExchange I'm diving into integral calculus for the first time and I have a few questions about this problem. A steel ball bearing at rest is accelerated in a magnetic field in a line with ...
1
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1answer
19 views

Sound and decibels at distance

If I have an object that is 53 decibels at x distance, how many decibels would y objects be at the same distance x, assuming they all created 53 decibels.
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2answers
37 views

Calculating velocity of an object moving at 12m/s north, with 5m/s wind from the west

An object moving 12m/s passes north and hits an object. Due to the wind from a west direction, it is pushed sideways at 5m/s. Find the resultant velocity. I don't know where to start with this one, I ...
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2answers
89 views

Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Let $\Omega$ be a region in $\mathbb{R}^2$ with $f:\Omega \to \mathbb{R}$ a smooth function. Why is the quantity, $$ \tfrac{1}{2} \iint_{\Omega} \|\nabla f\|^2 $$ Called the "energy" of $f$? I am ...
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1answer
33 views

Trigonometry in projectile motion

I initially posted this question on Physics SE but got no responses probably because it's more related to maths than physics. A plane surface makes an angle $\bf X$ with the horizontal. From the ...
0
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1answer
28 views

How to prove the Hubble law is the unique expansion law compatible with homogeneity and isotropy?

In the book physical foundations of cosmology, it saids that Hubble law is unique and a problem seems to be a hint of proving that. In order for a general expansion law,v=f(r,t), to be the same ...
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3answers
42 views

By how much should the distance from the source be increased to reduce the surface illuminance to 30 lumens?

This is my problem and I have no idea how to solve it: The illuminance of a surface varies inversely with the square of its distance from the light source. If the illuminance of a surface is 120 ...
3
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0answers
63 views

My orbiting body is orbiting about the wrong focus of it's elliptical orbit… why? [closed]

I am coding in c++ and am computing the position of an orbiting body as a function of time. Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it ...
1
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1answer
56 views

Question regarding combinatorics of resistance network. [closed]

If you have $N$ $1$Ohm resistors, how many distinct equivalent resistances can you create? Assume that only parallel and series and mixture of them is allowed and no bridging between two parallel ...
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5answers
54 views

Vector field ${\bf F}$ with $\int_S {\bf F}\cdot{\bf n}\ dS=c$

Find a vector field ${\bf F}$ on $ {\bf R}^3$ with $$\int_S {\bf F}\cdot{\bf n}\ dS=c > 0 \tag{1} $$ where $S$ is any closed surface containing $0$ and ${\bf n}$ is normal Here there is a ...
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0answers
39 views

What is the density of a homogeneous disk with mass $m$ and radius $a$?

Could someone help me understand why the density of a homogeneous disk is $\dfrac{m}{(\pi a)^2}$? I am trying to understand an example about finding the moment of inertia of an object. The question ...
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0answers
28 views

translating vectors in polar coordinates to the complex plane [duplicate]

These equations model circular motion. Equation R is the position vector given in polar coordinates. What I've done is represent this vector onto the complex plane via equation (1). Equation (2) and ...
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0answers
42 views

Derivation of the equations for non-uniform circular motion using complex analysis.

Here http://farside.ph.utexas.edu/teaching/301/lectures/node89.html They use complex analysis to derive the equations of non-uniform circular motion. My confusion is this: In the derivation they ...
4
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1answer
60 views

A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...
3
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2answers
136 views

Gödel's incompleteness theorems

In the last paragraph of Stephan Hawking's speech "Godel and the End of the Universe", he mentioned "... I'm now glad that our search for understanding will never come to an end, and that we will ...
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0answers
33 views

Subject to in equation

I have the formula below: $$\hat x_2=\arg\min\lVert x\rVert_2\quad\text{subject to}\quad A{x}=y.$$ But I didn't understand what was meant by "subject to" ? does $x$ is replaced by $x_2$? please can ...
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5answers
767 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
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1answer
91 views

Help with polar coordinates for physics problem

I need to solve a physics problem but don't know about polar coordinates properly, can anybody help with it? Suppose a curve which is a current carrying wire: $$r=\frac ...
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1answer
40 views

How to find the integral of $\int \frac{GMm}{r^2}\,dr$ [closed]

I want to find the integral of: $$\int_R^\infty \frac{GMm}{r^2}\,dr$$
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1answer
42 views

Why can we make this integral change of limits? Is it obvious?

When deriving the equation for the impulse-momentum theorem, the following occurs: $$\cdots=\int\limits_{t_1}^{t_2}\frac{d\vec p}{dt}dt = \int\limits_{\vec p_1}^{\vec p_2}d\vec p=\cdots$$ I know the ...
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2answers
81 views

Books that integrate physical reasoning with mathematical reasoning? mathematicians?

As the title says, can anyone help me to find any book that shows how physical reasoning using concepts from classical/quantum mechanics and physics in general can enlighten us about mathematical ...
10
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2answers
180 views

Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ...
4
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0answers
43 views

How to integrate scalar field over quarter torus? Infinite series does not converge.

This seems to be physics question, but the problem just concerns math. Preface If one wants to calculate the permeance $P$ of a rectangular bar: it is an easy task: $$P = \frac{\mu a b}{L} ...
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0answers
48 views

Derivative with respect to a vector and tensor on a manifold

I am reading through a paper and have come across a statement which I do not fully understand. I paraphrase below. Consider a scalar function $f = ...
0
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1answer
37 views

How to show $\psi^*(x,-t)$ is also solution of the Schrodinger equation

I've seen it stated that it "can easily be seen" that if $\psi(r,t)$ is a solution of the Schrodinger equation : $ih \dfrac{\partial \psi(r,t)}{\partial t} = H \psi(r,t)$, then $\psi^*(r,-t)$ is also ...
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0answers
20 views

Basis representation for non-negative, compact support, reasonably smooth spectral function

I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis ...
2
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0answers
46 views

Calculating work [closed]

How much work is required to lift a $1000\mathrm{kg}$ satellite from the surface of the earth to an altitude of $2\times10^6$ meters? The gravitational force is $F=\frac{GMm}{r^2}$, where $M$ is the ...
2
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1answer
60 views

Solving weak 2 body problem

I tried to solve a physics problem about two body problem where the masses $M$ and $m$ are $M \gg m$. The body $m$ is at radius $R$ from the mass $M$ and is falling down with initial speed $v(0) = 0$. ...
0
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1answer
50 views

Are distance-related paradoxes limited by the size of an atom?

See these 2 paradoxes: Coastline paradox The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. ...
2
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0answers
31 views

Can a quaternionic Kähler manifold be NOT Kähler?

I have an explicit construction of the metric on the quaternionic Kähler manifold $$\mathcal M = \frac{Sp(1, 1)}{Sp(1) \times Sp(1)}.$$ Arranging the four real degrees of freedom into two complex ones ...
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0answers
29 views

Properties of functional integration

this question comes from theoretical Physics, the issue being the so called Path Integral. The measure of this thing is something written as $[d\phi]=\prod_x d\phi(x)$ And this should be the limit ...
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0answers
23 views

Stopping angular momentum to obtain a particular angle

While the overall project relates to software development, it boils down to a simple (i think) physics problem. I have a joint (a motor, pretty much.) that needs to move to a specific angle. I can ...
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3answers
63 views

Maxwell's Equations Divergence Question

$$ \left\{ \begin{align} \text{div } \textbf{E} & =0, \\ \text{div } \textbf{H} & =0, \\ \text{curl } \textbf{E} & = \frac{-1}{c} \frac{\partial \textbf{H}}{\partial t}, \\ \text{curl } ...
0
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1answer
47 views

Maxwell's Equations Curl Question

$$\left\{ \begin{align} \text{div } \textbf{E} &=0, \\ \text{div } \textbf{H} & =0, \\ \text{curl } \textbf{E} & = \dfrac{-1}{c} \dfrac{\partial\textbf{H}}{\partial t}, \\\text{curl } ...
0
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1answer
35 views

Triangulation in delayed loudspeaker setup

I could use some help with the following situation. Two physically displaced speakers need to arrive on time, in order to achieve summation, for a given position (green dot) within a listening plane ...
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2answers
32 views

Calculating appearance of size of object at given distance

Here's the problem I'd like to solve. If I'm 1 ft away from a computer screen and a word on the screen appears a certain size, is there an equation or calculation that will tell me how big that ...
2
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0answers
76 views

Why is Grassman integration so weird?

Why are Grassman integration and differentiation equivalent? The only justification of this definition I have ever scene is "Well, how else could it work?" Indeed, I don't have any other suggestions, ...
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1answer
23 views

differential in integration cancelled but variable endpoint is changed

In kinetic energy equation in wiki. I have difficulty problem how endpoint in integral change from t to v. This doesn't look like it is using substitution method. ...
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0answers
39 views

derivation of an equation involving the Fourier transform of the square modulus of a wave function

A textbook on electron optics states that, ignoring a factor of 2 for convenience, the result $\mathscr{F}(I(\vec{r}))=\mathscr{F}(\phi(\vec{r}))\cdot{}A(\vec{k})\cdot{}\sin[\gamma(\vec{k})]$ can be ...
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0answers
34 views

Where are the time dilatational effects of orbital motion and gravitational acceleration equal?

This might not be the right forum to ask this question, but it is very interesting. Nearly four years ago, upon hearing of the observation of time dilation in two optical atomic clocks at an ...
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3answers
62 views

integral of the sphere describing lambertian reflectance

A Lambertian surface reflects or emits radiation proportional to the cosine of the angle subtended between the exiting angle and the normal to that surface. The integral of surface of the hemisphere ...