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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88 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
124 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
153 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
18 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
37 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
42 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
60 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
82 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
28 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
35 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
56 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
27 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
26 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
62 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
95 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
39 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
30 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
44 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
27 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
104 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
9k views

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
29 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
71 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
98 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
67 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
70 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
70 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
87 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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24 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
78 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
78 views

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 ...
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1answer
30 views

need to construct a function satisfying wave equation.

I need an example of a function that satisfies wave equation and that vanishes beyond certain range. I mean if $f(x,t)$ is a function of space and time, then $f(x, t) = 0, $ for $x < a(t) $ and ...
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1answer
105 views

How were the solutions to these differential equations found?

These two very strange differential equations came up yesterday while I was doing a physics problem that I made up: EQ 1) $y'^{2} = k \sin(y)$ EQ 2) $y'' = k\cos(y)$ where $y'$ means ...
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1answer
61 views

Divergence Free Vector Fields that are undefined at the origin

I am aware of vector fields which are undefined at the origin but whose divergence everywhere else is 0. In particular, my students have already seen the inverse square vector field, i.e. ...
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1answer
82 views

Platonic solids and charged particles

It is known that there are five Platonic solids: If, lets say, there are 4 particles with the same electricity charge and whose movement is constrained to be on a sphere, resulting forces will ...
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1answer
57 views

Free Vibrations - Simple Harmonic Motion

As an engineering enthusiast I have been practicing with numerous model assignments to see how well I could deal with dynamics if I were in an educational environment. Most problems seem simple to ...
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3answers
38 views

Calculating speed of free fall object

do i use this formula h=0.5gt² ? Given height is 9144mm (30,000ft) Given weight is 60kg how do I find the speed of falling? and time taken to reach the ground.
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2answers
25 views

Find the units of measurement of constant from formula

$$m\frac{dv}{dt}=mg-kv^2$$ $v=\ms^{-1} $m=kg$ $g=ms^{-2}$ $v^2=(ms^{-1})^2 I re-arrange the formula to isolate K $$K=-\frac{m\frac{dv}{dt}}{v^2}+\frac{mg}{v^2}$$ Sub in the units ...
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46 views

Invalid use of the analytic continuation of the Riemann zeta function?

Watching this video on You Tube I got the impression that some sciences (in this case physics) use the analytic continuation of the Riemann zeta function without justification. Maybe this is just my ...
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1answer
77 views

derive an equation for this mass spring damper

derive an equation to represent this mass spring damper in terms of input fore $F$ and relates to output displacement $(x)$ when springs $K_1=3$ , $K_2=5$ damper $C=6$ and mass $M=1$ , $F$ is a step ...
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2answers
29 views

Show that the velocity of the particle is… (Newtons Law question)

A particle of mass m is released from rest from height of ten metres above a body of viscous fluid. Show that the velocity of the particle at the moment of impact with the fluid is $14\text{m ...
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The phase plane and potential energy

I think I have spotted a mistake in my notes, however I need help verifying my assumption: I am given the equation: $d^2s/dt^2=-s$ m=1 for simplicity I have recast it at a first order system: ...
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1answer
25 views

Finding units of measurement of coefficients in ODE's

If we have a question where we have to find the coefficient's units such as K in this case. The actual formula contains more parts but it is simply the derivatives that I am unsure about. ...
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2answers
36 views

A object was fired from ground with initial angle $\theta$

so i got that , a object was fired from ground with angule $ \theta $. when the object get the height equal to half of his max height , the velocity of object is $\frac{3}{4}$ of initial ...
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2answers
66 views

Time period for simple pendulum without trigonometry

The time period for simple pendulum formula that is $t = 2\pi \sqrt{\frac{l}{g}}$ is valid only for $15^\circ$ of amplitude. Why not more than that? How do I explain this someone who has just been ...
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1answer
25 views

Amount of Liquid in Container

Given: a cuboid container, of dimensions h into w into l a rate of flow of liquid per unit time through an inlet, in a rate of flow of liquid per unit time from an outlet, out, when the container ...