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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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
58 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
106 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
110 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
193 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
118 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
55 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
37 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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3answers
43 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 ...
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0answers
74 views

Are there any legitimate examples of applications of set theory to Physics?

Sets are of course ubiquitous, so in this sense set theory is applicable to physics. But I'm thinking more like techniques like forcing, or constructs like cardinals or ordinals. Intuitively it ...
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2answers
25 views

How do you scale the change of a period over time?

I am writing a game, and I have a period (a repeating cycle) which is mapped to the scrolling of a background. I want to change this period, so that the scrolling is faster or slower--- but if I just ...
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1answer
38 views

Decaying velocity model

I am reading a paper that goes: Here tau accounts for timing and sensor inaccuracies (inherent of the operating system available on mobile phones) by providing a decaying velocity model, ...
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3answers
91 views

Moments at which moving points on a circle coincide

Points A $(0,1)$ and B $(1,0)$ start moving along the circumference of a unit circle with center $(0,0)$ in the same, positive (that is, counterclockwise) direction. Every minute, points A and B ...
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1answer
39 views

finding the mass and number of atoms

A small cube of iron is observed under a microscope. The edge of the cube is $4.00 \times 10^{-6}$ cm long. The atomic mass of iron is 55.9 u, and its density is 7.86 $g/cm^{3}$. a) Find the mass ...
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1answer
77 views

I can't seem to find this derivative any help would be great.

A rocket of mass m = 1000 kg is traveling in a straight line for a short time. The distance in meters covered by the rocket during this time is described by the function $r(t)=t^3 −3t^2 +6t$ where ...
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1answer
84 views

Does pure math have anything to say about the Lorentz transformation?

The Lorentz factor, $${1 \over {\sqrt {1 - {{{v^2}} \over {{c^2}}}} }}$$ appears intuitively correct from a mathematical viewpoint. According to special relativity, the ratio of the velocity of a body ...
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2answers
90 views

how to calculate vehicle speed using mathematics and Image processing?

i am doing my project in image processing.using segmentation i have detected the moving part(i.e the car) in the video successfully. But now i want to calculate speed of vehicle. in the above ...
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2answers
143 views

Is there a deeper meaning when a number is squared? [closed]

In my opinion, math is about more than just memorizing equations, it's about numbers that are built in a way that represents our understanding of something. So I ask this, what does it mean ...
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1answer
16 views

How to find time of man running? (motion formulas)

So for this question there is a man running through a section of grass 1.14375m long at a speed of 3m/s. How do i find his time do i assume the initial velocity is 0? Because that is the only way it ...
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1answer
35 views

Transpose of a differential operator

Let $H$ be a diagonalizable matrix (not necessarily Hermitian). Then, it induces a biorthogonal left and right vectors, such that $$ ...
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1answer
39 views

Scale-invariance of $\int_0^\infty \frac{f(x)}{x} \ dx$

Let $f$ be some non-negative, measurable function on $[0,\infty)$. The quantity $\int_0^\infty \frac{f(x)}{x} \ dx$ is scale-invariant in the sense that, if one puts $f_c(x) := f(cx)$ for $c > 0$, ...
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1answer
57 views

Programming constraints in video game. How are these two equations equal?

I'm currently working on programming a game that uses a physics engine (NAPE). Inside of that engine there are constraints that you can program. In order to program those you need a somewhat ...
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1answer
59 views

Force between two parallel wires?

Having two current carrying (currents $I'$ and $I$) wires of length $a$ parallel to the $z$-axis, one with end points $(0,0,0)$ and $(0,0,a)$ and one from $(a,0,0)$ to $(a,0,a)$, I'm looking for the ...
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4answers
69 views

Multiple choice question on rates of change (or so I thought)

If I were to find the resistance of the component (see image below), I would either find the equation of the curve and use differentiation or I'd draw a tangent at $V_2$ and then find the reciprocal ...
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1answer
16 views

Meaning of multiplication by $\sin$ in $\omega$-domain

Multiplying some signal, a function of time, $m(t)$ by a cosine $\cos{\omega' t}$ causes a shift in frequency of $m(t)$, by $\pm\omega'$. But what about multiplication by a sine wave, such ...
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1answer
25 views

Angular momentum, rotating rigid bodies, simple example…

Revising, this is what I'm stuck on: inertia tensors, rotating rigid bodies about axis other than its axis of symmety,... I think it'd help a lot to see a worked example and I can't find anything on ...
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1answer
50 views

Two particles moving at consant velocity: how close do they get?

A particle was at point $P_1$ at time $t_1$ and is moving at the constant velocity $\vec{v}_1$. Another particle was at $P_2$ at $t_2$ and is moving at the constant velocity $\vec{v}_2$. How close did ...
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1answer
23 views

Divergence Computation in Gauge Theories, Knots and Gravity

Hopefully this is just some minor confusion...The first exercise wants us to show that $$\vec \epsilon(t,\vec x)=\vec Ee^{-i(wt-\vec k \cdot\vec x )}$$ satisfies the vacuum Maxwell equations where ...
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0answers
15 views

Separation of the centre of mass coordinates for an N-electron atom

Can anyone tell me how to derive [A8.5] and [A8.6] in Appendice 8 of "Bransden: Physics of solid state matter", in this screenshot: http://i.imgur.com/zSCkVnI.jpg ? It should be easy, but damn me I ...
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0answers
24 views

Angular momentum, rotating cylinders,…

Revising, this is what I'm stuck on: inertia tensors, rotating rigid bodies about axis other than its axis of symmety,... I think it'd help a lot to see a worked example and I can't find anything on ...
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2answers
61 views

Proof that energy of a free body is constant, using the derivate

Ok, what I'm trying to prove is the law of conservation of energy for a free fall. Let the downward direction be positive. We want to prove that: $$mgh+\frac{mv^2}{2}=constant$$ For this, we try to ...
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1answer
92 views

numerical update rule for discretized hawkes excitation process

So I think I am just misunderstanding some simple notation or something and would appreciate some help. I am trying to replicate this model in an agent based model, but I cannot seem to figure out the ...
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2answers
37 views

simple question about $\nabla r$

In my physics notes, it says $\nabla r = \underline{e_r} = \frac{\underline{r}}{r}$ and $\nabla \frac{1}{r} = - \frac{\underline{r}}{r^3} = - \frac{1}{r^2} \underline{e_r}$ I don't quite ...
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0answers
25 views

Newton's differential equation

As we all know one of Issac Newton's many achievement was to use his theory of gravitation and his law of motion to determine the way the planets move. I am looking for a not too deep resource in ...
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0answers
37 views

Integration in physics and calculations with $dx$

I'm in a physic formation and we are used to play with the infinitesimal elements $dx$ of integration like a variable (for example the calculation of the pressure of a gas), because we look at small ...
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2answers
39 views

Calculate the energy in a circuit containing a resistor

A voltage peak in a circuit is caused by a current through a resistor. The energy E which is dissipated by the resistor is: Calculate E if Can anyone please give me some suggestions where to ...
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0answers
25 views

plane wave move out

I have a plane wave that is recorded by a set of receivers with x spacing between them (see the sketch). in the sketch (plane wave in black slant line, receivers are the little circles in black and ...
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1answer
44 views

Determining the ratios needed in gear reduction

I am trying to work out the math behind building a gear box for turning a gear a specific RPM from a small motor. Given that a typical DC hobby motor turning at 200 RPM, and a target in the final ...
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10answers
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Why can't you add apples and oranges, but you can multiply and divide them?

What is the algebraic difference between arithmetic operations, that prevents entities with different units from being summed or subtracted, but allows them to be multiplied or divided? This looks ...
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0answers
26 views

Dhar's Burning Test - Confusion about Abelian Sandpile Model

Dhar's Burning test is a bijection between the spanning trees of a certain graph and the recurrent states Abelian sandpile model. I would like some help working out this bijection in different cases: ...
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1answer
54 views

Fourier-Laplace Transform of Heaviside Step function multiplied to Sine

In a Advanced Solid State lecture I encountered the following assertion- Fourier Transform of $\Theta(t)\sin(\omega_0 t)$ is ...
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3answers
92 views

What's the term for a “physical vector space”?

In physics, we often use the term "vector space" (or just "space," or other similar terms) to refer to a vector space in which the different dimensions are "compatible," i.e. that it "makes sense" to ...
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1answer
66 views

Please, as possible, explain in layman's terms: What is a discontinuous space?

What is a "discontinuous space"? Is it synonymous of "discrete space"? I searched in Google but did not find an accessible explanation. I have an idea of it as a space where all lengths are multiples ...
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4answers
60 views

Proof: Force always perpendicular and motion in a plane implies that the trajectory is a circle

I am looking for a proof for a physics problem. Consider a particle which is subject to a force $\vec{F}(t)$ with $|\vec{F}(t)| = \text{const}$ which is always perpendicular to the velocity ...
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1answer
59 views

Uniform Circular Motion with Banked Road and Car

In Uniform Circular Motion, if a car is rounding a curve at a certain speed, and the angle of the road allows the car to drive around at that speed, that speed is called the "design speed." If the ...
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3answers
40 views

Calculate initial velocity to reach height Y

I am working on a program that shoots a projectile straight up into the air. I need to be able to calculate the initial velocity required to reach height Y. Assume there is a gravitational constant of ...
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0answers
22 views

Is it possible to simulate fluid dynamics in a time-based and deterministic manner?

The Problem Domain I have a number of network-connected PCs. I want to be able to simulate and replicate the same simple fluid dynamics simulation (Eg Navier-Stokes), in real-time, between them. That ...
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1answer
73 views

Intuition for Integration of Differential Forms

In mathematics, we define $dx^i$ as linear functionals, when speaking of integration. However, in physics, we interpret $dx^i$ as very small quantities. There is nothing inherently small about a ...
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1answer
85 views

Determine the location of multiple static bodies based on their “gravitational” effect upon a dynamic point?

I am writing a SF story, and though I'm sure that I've violated most of science and math to the Andromeda Galaxy and back, I'd like this part at least to be mathematically accurate. Here is a run down ...
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0answers
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Could this be called Renormalization?

Quoted from   Space-Time Approach to Quantum Electrodynamics   by R. P. Feynman, Phys. Rev. 76, 769 1949 : We desire to make a modification of quantum electrodynamics analogous to the ...