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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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 } ...
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1answer
46 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 } ...
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0answers
17 views

What force counteracts friction when a block is pulled? [migrated]

Firstly, I understand and apologize that this is more of a physics question than a math question. I noticed that when I pulled a book out from under a pack of gum, the gum stayed largely in place (it ...
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1answer
33 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
30 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 ...
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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
20 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
32 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
53 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 ...
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0answers
50 views

ODE particular solution (physics)

I have to do this exercise: ($Z(t)=I(t)$, it's printed wrong). I have a doubt about the first item. To find all resonance when $R=1$, I found the particular solution $I_{p}(t)=A\sin(\omega ...
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0answers
40 views

Angular displacement/speed of a rotating sphere from 3d points

I have 3d points on the surface of a unit sphere that describe every minute its rotation. I want to know angular velocity of this sphere. The sphere center is fixed and the axis of rotation can change ...
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1answer
40 views

Word Problem, Calculus estimation homework

Roger runs a marathon. His friend Jeff rides behind him on a bicycle and clocks his speed every 15 minutes. Roger starts out strong, but after an hour and a half he is so exhausted that he has to ...
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1answer
59 views

Partitions applications in physics

Is there any direct application of all developments related to partitions? I am specially interested in physics but cryptography or other mostly theoretical areas would also be a good answer. By ...
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2answers
91 views

Solution of differential equation with Dirac Delta

Is it possible to solve a differential equation of the following form? $\partial_x^2y + \delta(x) \partial_x y = 0$ where $\delta(x)$ is the dirac delta function. I need the solution for periodic ...
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1answer
43 views

How to properly generalize a definite integral?

I know, I know. On the can, this problem seems simple. Just take $\int_a^bf(x)\mathrm{d}x$ and write is as $\int f(x)\mathrm{d}x$. However, when I tried to do that on an Engineering Dynamics ...
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3answers
51 views

Rate of change question (planes, kites and the such)

Q: A kite $100 \ m$ above the ground moves horizontally at a speed of $8 \ m/s$. At what rate is the angle between the string and the horizontal, i.e. e the ground, decreasing when $200 \ m$ of string ...
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1answer
60 views

Formulation VS Interpretation

I'm reading a book on Mathematical Physics and at some point the author says that we must distinguish between a "formulation" and an "interpretation" of a theory, although it's not easy to point what ...
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1answer
26 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
2
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1answer
67 views

How we apply representation theory to physics.

I want to have a concrete idea of what people do with representation theory in physics. Here is what I think: Corresponding to a specific "physics", there is particularly a Lie group (called G) of ...
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0answers
11 views

Inter-neighbor resistance on triangular prism

Given a triangular prism of infinite length along the X direction. A graph is formed with the set of nodes all the points on an edge of the prism with integer values of X, and the with each node ...
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3answers
70 views

Representation theory in physics

0 down vote favorite I'm sorry if this is somewhat a dumb question. First: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements ...
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1answer
32 views

How far will my car roll given a function representing the slope of the landscape I'm driving on?

So I was driving in my car thinking to myself "I wonder how far I would go (before starting to roll backwards) if I just took my foot off the brakes" I tried to figure it out myself but could not. SO ...
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1answer
52 views

Why do these acceleration computations contradict each other?

A rocket follows the path $(y-40)^2=160x$ after traveling vertically to the height of 40 feet (making for a very convenient continuity. The problem asks "If the component velocity in the vertical ...
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1answer
23 views

Calculating the force on each of two directions needed to move object to destination

Given the following: How would you calculate the forces needed on the v and u directions to move point ...
2
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2answers
47 views

Differentiation of function

There is a passage in a physics textbook I don't quite follow. Since my question is mathematical, I've decided to post it here. The book says: Let $V$ be the volume of a molecule and assume $V = ...
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1answer
19 views

Evolution curves on dynamic system

The matrix of a linear dynamic system is: [0, 3] [3, 0] FACT: If A is the evolution curve that passes on point (1,1) in phase space and B the evolution curve that passes on point (1,-1) we can ...
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0answers
60 views

Resources for learning Relativity

I´m looking for books to the study of Relativity. I know that this is math stack schange and not physics stack schage, but I believe that some of the users here are interesed in physical-mathematical ...
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3answers
163 views

Is speed a function of position?

Let $x$ be a smooth function from $[0,\infty)$ to $\mathbb{R}^n$ satisfying the following differential equation $x''(t) = f(x(t))$, where $f$ is a smooth function from $\mathbb{R}^n$ to itself. Then ...
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1answer
40 views

Centre of Mass and Moment of Inertia of a sphere - spherical cap

I have been given a sphere of radius a, from this sphere a cap of hight h is cut off. 1) What is the centre of mass of the rest of the sphere? 2) What is the moment of inertia regarding the axis of ...
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2answers
57 views

is it necessary that curl of 2d vector is perpendicular to the plane.

I am just confused, help me guys. The question comes up, because we say that curl is either clockwise or anti-clockwise at a point.
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1answer
69 views

How to prove that something is finite

I'm given a physical model of something. Say it's a radius of a planet: $$R=\pi\left(\frac{n}{2\pi G}\right)^{1/2}$$ where $G$ is the universal gravitational constant, n - "positive constant" If I ...
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3answers
56 views

Minimum speed using calculus

I've been trying to answer this question , specifically part c) I've done part a) and b) where $U = \frac{28\sqrt{15}}{15} $ and $ \theta = 53.3 $ degrees . For the last part I need to work out the ...
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0answers
110 views

If physical space had cardinality larger than $\aleph_1$, would we need new math to describe dynamics? [closed]

If physical space had cardinality larger than $\aleph_1$, would we need new math to describe dynamics? For instance, would the dynamics of a sea of virtual particles of cardinality $\aleph_1$ would ...
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1answer
22 views

Differential problem in Gausses law

From the Gauss law we know, $\nabla \cdot \vec{E} = \rho / \epsilon_0 $. We have given that, $\vec{E}= kr^3 \hat {r}$ Now I have problem to get the identified part. Can you please elaborate ...
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0answers
24 views

good primer or intro on quenched stochastic processes

I was hoping that someone could recommend a good intro to "quenched" stochastic processes. I am using quenching in the sense of condensed matter physics where systems can present quenched disorder.
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1answer
24 views

Limiting a energy term

A famous Einstein's mass energy equivalence equation is $E= \frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$ I need to prove from the above equation is that E = pc. I know that, i will have to limit $m ...
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2answers
38 views

Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
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2answers
51 views

Finding the average of the absolute value of a function?

I know that to find the absolute value of a function, $$\frac{1}{b-a}\int^b_af(x)\mathrm{d}x$$. This is actually kind of intuitive. The problem is I don't know how to to find the average of the ...
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2answers
42 views

Calculate Displacement when velocity is a function of displacement

Particle is moving on a straight line and where velocity varies with its displacement as $v=\sqrt{4+4s}$. Find displacement at t = 2 s if s=0 at t=0. I am not able to figure out how to approach this. ...
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1answer
31 views

How can I read logarithmic scale?

I've got this histograms: How can I read that logarithmic scale? For example, on the histogram 1 there is approximately $10^{-3}$ value at y-axis at 2 value at x-axis. Does it meant that there is a ...
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4answers
78 views

Euclidean Geometry in Physics

I've started tutoring my 13 year old niece in math. She learning geometry this year (it's a year-round school). Obviously, it'll just be basic Euclidean geometry -- though I might try to get to a ...
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1answer
60 views

Mathematics/Mechanics Problem

I would like to ask you if anybody could help me with this problem. So far i know that the positions where B and A have to meet are at distances L and L+2r
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1answer
109 views

Please explain the logic behind $d(xy) = y(dx) + x(dy)$

I've seen $d(xy) = y(dx) + x(dy)$, but I don't understand the principle behind it and memorizing it is lame. Can anyone explain what is going on here? For example from physics, $$F = {{dP} \over ...
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2answers
130 views

List of Advanced Math Text Books with answers

Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of ...
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2answers
196 views

Seasonal changes in hours of daylight

I will post my own answer to this question unless someone else posts the same answer first, but I am curious to know what other points of view might lead to different ways of answering it. ...
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0answers
134 views

How to solve a time-dependent Schrodinger equation in periodic Dirac delta potential

I'm trying to solve a 1D time-dependent Schrodinger equation: $$ i\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} \frac{\partial^2}{\partial x^2}+V(x)+F(t)*x\right]\psi(x,t) $$ where $V(x)$ ...
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1answer
60 views

Calculating a double pendulum

consider the following situation of a double pendulum. We found the moving equations as $$ \ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\sin(\theta_2-\theta_1),\\ ...
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0answers
38 views

Why is the space of trajectories for a particle a cotangent bundle?

In Paugams book, Towards the Mathematics of Quantum Field Theory, he writes the following in the introduction: Let us first illustrate this very general notion by the simple example of Newtonian ...
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1answer
50 views

Solving 2nd-order ODE for SHO

In physics for a Simple Harmonic Oscillator, we have the differential equation $$ {\frac {d^2x}{dt^2}} + \frac kmx = 0 $$ from the balance of forces, which has a solution $$ x(t) = {x_o}\cos(\omega ...