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
38 views

Acceleration: If I know distance, time, and initial velocity, what's acceleration and final velocity?

So I know the Initial Velocity ($V_i$), Time ($t$), and Distance ($d$). I know that $$d = V_it + \frac{1}{2} at^2$$ If I rearrange this, would acceleration $a = \dfrac{2(d - V_it)}{t^2}$ ? Then ...
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1answer
17 views

Trigonometric function with a theoretical scenario used to find missing variables?

For my pre-calculus class I am given a theoretical scenario and I am tasked with finding the different time(s) an object within the scenario will be "x" inches above equilibrium. The prompt given to ...
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0answers
25 views

Power of a signature (sum of squares divided by number of elements)

I need to find some literature to study the theory of an exercise I am working on (it is from a course in digital image processing and pattern recognition). I have an $n\times n$ matrix, I have to ...
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0answers
38 views

How a “pillbox” can be considered as a Gaussian surface?

I'm currently practicing how to use Gauss's Law to evaluate electric flux passing through a Gaussian surface, but how a "pillbox" can be considered as a Gaussian surface, although it is not a smooth (...
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0answers
22 views

Question about forever acceleration on a pendulum

So i'm a bit confused about something. If we take a mathematical pendulum and we apply a force to it. We ignore all friction and air resistance and only consider gravity and the force applied to bob. ...
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15 views

Finding the electric and magnetic field outside a cylindrical conductor.

A cylindrical conductor with constant circular cross-section and uniform conductivity $\sigma$ has a steady current I that is uniformly distributed across the cross-section flowing through it. Find ...
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1answer
69 views

Kinetic energy of incompressiblue fluid

I am trying to show that the kinetic energy for an incompressible and irrotational fluid with no sources and no sinks is given by $$\frac{\delta}{2} \iint_{S} \psi \frac{\partial \psi}{\partial n} ...
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1answer
35 views

Book's for potential theory: single and double layer potential

Does anyone know recommend me some book about the theory of the potential, especially that concerning the layer potential. Besides the theoretical part in the higher dimension, if there are concrete ...
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0answers
15 views

Circulation around a curve

in a previous question I had asked How to apply the divergence thereom in the plane About the divergence of $F=(xy)i+(2x-y)j$ where C is the triangle with verticies $(0,0)$ , $(1,0)$ and $(0,1)$. ...
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1answer
27 views

Units of $F(x) = x-x^3$

If we are given that $F(x) = x-x^3$ is a force function, which means it is in the units of $[M][L][T]^{-2}$, then how do we determine what kind of "unit units" participate in this function? Namely, ...
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47 views

Recommendations: Any Good books to study Path-Integration from 0 again?

I was researching and talking with some friends about I want to start from zero studying path integral, this question, and they recommended I start by studying "Quantum Mechanics and Path Integrals". ...
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1answer
49 views

What am I doing wrong when I try to deduce the Laplace transform formula?

The Laplace transform of a function $f(t)$ is the projection of $f(t)$ vector (indexed with $t$) onto the linearly independent set of vectors $e^{st}$. The projection of a vector $\vec{v}$ onto ...
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1answer
42 views

Associated Legendre Polynomials Orthogonality Proof

I have to solve the following equation using associated legendre polynomials, $\int_{-1}^1 P_k^m(x) \cdot P_l^m(x) \; \mathrm{d} x = \frac{2(l+m)!}{(2l+1)(l-m)!} \delta_{k,l}$ Where they are ...
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1answer
23 views

Associated Legendre Polynomials!?

Is there someone who can maybe just explain what these associated legendre polynomials are. I have studied about the Legendre Polynomials but I can not understand how these are used in Schrodingers ...
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1answer
28 views

Determining the most appropriate set of eigenmodes for a modal decomposition of an experimental data set

I have a complex vector of the transverse amplitude and phase distribution of a laser beam, derived from experimental data. When modelling these field distributions, ordinarily the eigenmodes of the ...
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0answers
38 views

Optimising 2D acceleration to intercept a moving target

Related to this question: Accelerating one moving body to intercept another body in 2d I have a spaceship that needs to intercept a moving target in 2D. They have a relative velocity and I need to ...
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1answer
30 views

Accelerating one moving body to intercept another body in 2d

I have a spaceship moving in a 2D plane and wish to intercept another body which is also moving in the same plane. To do this I need to find a series of accelerations over a series of times that will ...
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0answers
42 views

Integrating the equation for change in entropy

In physics, the change in entropy is defined as $$dS = \frac{dQ}{T}$$ I tried integrating this. $$\int ds=\frac{1}{T}\int dQ$$ $$S=\frac{Q}{T}+C$$ This essentially converts the change in entropy to ...
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0answers
21 views

How to model the following scenario with an ODE if possible

Consider a cylinder, full of charged particles travelling through. From the perspective of looking through the tube, you would see a circle of particles and obviously this circle continues down the ...
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0answers
29 views

Which functions can be the resistance of a network?

Say we have $n$ resistors, with unknown resistances $r_1,\ldots,r_n$. We build a network using these, along with any finite number of other resistors of known resistance. We then measure the ...
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0answers
22 views

Time taken for a Mass on a Spring to Travel 7mm with constant friction and a force acting against it.

So I have been driving my self mad with this problem and I cant seem to deduce a logical answer any help would be greatly appreciated. Problem: I have a mass on the end of a compression spring. It is ...
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1answer
56 views

“Flow lines” of “dust” are geodesics?

The stress-energy tensor representing "dust" takes the form$$T_{ab} = \rho u_au_b$$where $u^a$ is a unit timelike vector field, i.e., $u^au_a = -1$. Does it necessarily follow that in any solution to ...
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1answer
116 views

Identity in general relativity, not sure if true or not

Let $(M, g_{ab})$ be a spacetime and define a new metric, $\tilde{g}_{ab}$, on $M$ by $\tilde{g}_{ab} = \Omega^2 g_{ab}$, where $\Omega$ is a smooth, positive function. Let $\nabla_a$ denote the ...
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4answers
63 views

How to solve $a = \cos x - b\sin x$ where $a$ and $b$ are real numbers?

I found this equation when solving a physics problem related to finding an angle when entering a river, that has a known current, and trying to get to a specific point on the other side. I'm not sure ...
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1answer
26 views

Does it necessarily follow that the integral curves of $k^a$ are null geodesics?

Let $f$ be a function on a spacetime $(M, g_{ab})$ whose gradient, $k_a = \nabla_a f$, ie everywhere null, i.e., $k_ak^a = 0$ throughout $M$. Does it necessarily follow that the integral curves of $k^...
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0answers
79 views

Diffeomorphisms vs symplectomorphisms / volume conserving diffeomorphisms in an application

This question needs a bit of background: one way to study the mechanics of deformation of a continuous solid body is by defining a reference body $B_0$, a connected, well-behaved subset of $R^2$ or $R^...
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1answer
32 views

Tips to find magnitude of 2 forces when given the magnitude of their resultant

Forces A and B has a resultant force C with magnitude of 200N. The magnitudes of A and B have the relation of 2||A||=3||B||. $\theta$ is the angle between A and C, and the angle between B and C is 2$\...
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1answer
28 views

How to diagonalize a Hermitian matrix using a quasi-unitary matrix?

I met a problem requiring the diagonalization of a $2n\times 2n$ Hermitian matrix $H$ in the following way: $U^{*} HU=D$, where $D$ is diagonal, $U^*$ is the transpose conjugate of $U$. The matrix $...
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0answers
31 views

Notation for variables representing complex numbers

Is there a standard way to indicate that a variable represents a complex number? In physics, it is convenient to analyze oscillating systems using complex numbers. The authors of one popular ...
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4answers
137 views

A Proportion Question

If $a$ is directly proportional to $b$ and also directly proportional to $c$, is it true that $a$ is directly proportional to $bc$.(It seems like it is true) Here is what I did and I have a feeling ...
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0answers
27 views

Infinitesimal canonical transformation

I'm not able to understand how they have simplified both the computations from the second line to the third. So in the first computation how did {ri,pl} become 1 in the third line and how did {pi,rk} ...
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0answers
36 views

Interesting derivation of the moment of inertia of a Ball

I was attempting to calculate the moment of inertia for a ball of radius R about the z axis when a mistake still led me to the correct answer and the seemingly correct method leads to the wrong answer....
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1answer
33 views

Stuck in using Stirling's approximation to show and justify an approximation of the number of permutations with and without ordering

This is a problem from my applied mathematics class where we are currently working on using Stirling's approximation which is: $ n! \sim (\frac{n}{e})^n \sqrt{2 \pi n} $ and the context of this ...
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1answer
25 views

Proof involving Poisson bracket

Not being able to understand how each term has been simplified to get from the third step to the fourth step. So how did 1/2m become 1/m and {qj,plpl}pk become {qj,pl}plpk and how did k/4 become k/2 ...
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1answer
61 views

A problem with calculus..

A body is dropped in a well and it travels $p$ depth in $t$ time interval. The relation is $$p(t)=\frac4{4+t^2}+0.8t-1.$$ Find the velocity and acceleration. Now if I differentiate the expression ...
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2answers
48 views

What's a method for computing the indefinite integral $\int \dfrac{dz}{(a^2 + z^2)^{3/2}}$?

This integral occurs in EMFT when computing $\overline{E}$ due to an infinite line, uniform charge distribution. I'm trying to figure out the formula for $\int\dfrac{dz}{(a^2 + z^2)^{3/2}}$, using ...
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0answers
25 views

How to do this Poisson bracket proof

For the proof of the above equation, I understand the first step which has been obtained from the definition but in the second step I don't understand why they are summing over $j$ first (shouldn't ...
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1answer
19 views

Poisson bracket proof

For this question I understand the first line of the solution which they have obtained from the definition but how have they simplified each term to get to the second line from the first line? The ...
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1answer
107 views

Is the regularization of a Fourier transform unique?

The Fourier transform of the Coulomb potential $1/\vert \mathbf r \vert$ of an electric charge doesn't converge because one obtains $$F(k)=\frac {4\pi}{k} \int_0^\infty \sin(kr) dr.$$ The standard ...
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0answers
21 views

decreasing travel time over an arc

I am trying to write a program that travels along the same arc but each iteration the travel time needs to decrease. I have been trying to do this by changing the starting velocity and acceleration. ...
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0answers
22 views

Elliptical orbits and differential unit angle? What's $d\hat{\theta}/d\theta$

I was reading a short article on the derivation of the elliptical orbits of bodies under the influence of inverse-square gravity, and it goes something like this: $m\frac{d\vec{V}}{dt} = m\frac{d\...
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1answer
32 views

Poisson bracket proofs

I understand the first sentence you wrote for the need of a different summation index. However, i'm still not able to understand the individual steps. Like how in the first line we have four partial ...
0
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1answer
28 views

Justification of manipulations used to solve a physics problem.

Problem. A particle moves in a deaccelerated manner, describing a circular trajectory of radius $r$, having an initial speed $v_0$. Suppose $a_n=-a_t$ (normal acceleration and tangential ...
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5answers
873 views

Why does adding a term $5f'(t)$ to $5f''(t)+10f(t)=0$ cause damping?

So we have a differential equation to model an oscillator: $$5f''(t)+10f(t)=0$$ Where the initial conditions are $f(0)=0$ and $f'(0)=4$. It is given that $f(t) = \frac{2\sqrt 2}{5}\sin\sqrt2 t$. ...
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3answers
27 views

Basic problem on deceleration

A car accelerates from rest for $15$ s with a uniform acceleration of $1.5$ m/s^2 and immediately decelerates with a uniform deceleration of $5$ m/s^2. How long does deceleration take? I used $v=u+...
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1answer
35 views

Can we interchange derivatives when multiplied?

Although this looks like a physics question, this is more of a Math question, I was reading the Energy-Mass relationship derivation, it goes as follows, Force $F$ is given by $$F=\frac{d}{dt}(mv)$$...
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1answer
51 views

Escape velocity

Calculate the escape velocity from a white dwarf and a neutron star. Assume that both the white dwarf and the neutron star is 1 solar mass. Let the white dwarf’s radius be $10^{4}$ kilometres and the ...
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0answers
21 views

What is the gravitational potential of an ellipsoid at $0$?

What is the gravitational potential of an ellipsoid at $0$? Given an ellipsoid: $\frac{x^2+y^2}{a^2} +\frac{z^2}{c^2} \leq 1,$ and a uniform density of mass: Using spherical coordinates, and the ...
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1answer
55 views

Simplifying a complex trigonometric expression

Context: In a previous question , I've stated I'm making a program that will be used for calculating stuff with Statics of a particle. I've come across another scenario in which there's three forces ...
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1answer
26 views

How to make vector from azimuth and speed?

I don't know how to make $3$D vector of speed from azimuth and speed. Azimuth is in degree and speed is in m/s. Azimuth is angle on $X$ and $Y$. Thank you for your help!