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

learn more… | top users | synonyms

4
votes
0answers
30 views

The Virasoro-Bott group and the KdV equations

The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group. For the famous $KdV$ equations these equations are given on the Virasoro-Bott ...
2
votes
1answer
29 views

Projectile motion: Proving:$ x^2 + 4 \left(y-\frac{v^2}{4g} \right)^2 = \frac{v^2}{4g^2} $

Question: Projectiles are fired with initial speed $v$ and variable launch angle $0< \alpha < \pi$. Choose a coordinate system with the firing position at the origin. For each ...
2
votes
0answers
80 views

how to solve this integral ? It seems bounded and well defined integral but I don't know how to solve this

how to solve the following integral ? It seems well defined i.e. bound but I could not solve it. I tried by expanding series expansion of tanh[x] but after that I got a series as an answer, which I ...
7
votes
3answers
429 views

What is the difference between |(d/dt)velocity| and (d/dt)|velocity| [Physical Interpretation] [closed]

According to me the modulus of $\frac {\text{d}v}{\text{d}t}$ gives the magnitude of acceleration without accounting for direction but I am stumbled on how to interpret ...
3
votes
0answers
19 views

Finding the work done, given a function.

A heavy metal 2 pound bucket initially is filled with 10 pounds of paint. Immediately after it is filled, it is pulled up at a steady rate to the top of a building 30 feet high. While being pulled, ...
3
votes
2answers
30 views

What does it mean to use levi civita symbol with Poisson brackets in this way

I'm doing some studies in mathematical methods for physics and I came across something that I don't really understand. I have only been using the $\epsilon_{ijk}$ when I cross some vectors or ...
1
vote
1answer
29 views

Calculus Compress Spring

I have a question I cannot seem to get correct and am looking for some help. Suppose a force of $40~\text{N}$ is required to compress a spring $3~\text{cm}$ from its equilibrium length. How much ...
1
vote
1answer
25 views

Numerical solver for maxwell equations?

Just curious if someone has come across a package where I can simply solve the basic maxwell equations(just the curl equations). I'm just interested in solving it on a 2-d plate out of interest. ...
0
votes
0answers
39 views

How much does water cool in 1 second

I'm wondering if I've done my calculations correctly because the units I get are really weird... So.. I'm calculating how much the temperature change in $1$ second if the temperature difference is ...
1
vote
0answers
35 views

Dynamics of fluid

While reading on Wikipedia about the partial differential equations (https://en.wikipedia.org/wiki/Partial_differential_equation), I wondered how dynamics for the fluid occur in an ...
1
vote
3answers
31 views

Relative velocity from points' point of view

Edit: The terminology might be imprecise. Please pay attention to the picture I drew to explain my problems. I will appreciate an edit that will ensure the terminology is no longer disputable. This ...
0
votes
0answers
33 views

Calculate initial velocity

If I have the equation $y'' = -g -by'$, I know that a rock was thrown straight up from a specific height h, and hit the ground at time t, how do I calculate its initial velocity? I don't understand ...
0
votes
1answer
34 views

configuration spaces in mathematics and in physics

On the Wekipedia website Configuration space , there are two configuration spaces defined. One is Configuration spaces in physics, the other is Configuration spaces in mathematics. Question. Do ...
1
vote
1answer
35 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 ...
0
votes
1answer
15 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 ...
0
votes
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 ...
0
votes
0answers
25 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 ...
0
votes
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. ...
0
votes
0answers
13 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 ...
1
vote
1answer
67 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} ...
1
vote
1answer
30 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 ...
0
votes
0answers
16 views

how to formulate an equation for this?(modified 3D sphere)

I was reading about a situation, where a sphere is close to a solid plane boundary. whose radius is 'a' and whose centre is 'a+b' away from the solid plane boundary. so they have a function h(r,t) ...
0
votes
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 $(0,1)$. ...
0
votes
1answer
25 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, ...
1
vote
0answers
45 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". ...
5
votes
1answer
47 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 ...
0
votes
1answer
34 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 ...
0
votes
1answer
18 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 ...
1
vote
1answer
27 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 ...
0
votes
0answers
27 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 ...
0
votes
1answer
27 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 ...
0
votes
0answers
35 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 ...
0
votes
0answers
19 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 ...
2
votes
0answers
25 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 ...
0
votes
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 ...
4
votes
1answer
48 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 ...
10
votes
1answer
110 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 ...
0
votes
2answers
47 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 ...
6
votes
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 ...
1
vote
0answers
77 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 ...
0
votes
1answer
29 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 ...
0
votes
1answer
25 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 ...
0
votes
0answers
25 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 ...
4
votes
4answers
135 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 ...
0
votes
0answers
22 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 ...
0
votes
0answers
35 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 ...
1
vote
1answer
28 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 ...
0
votes
1answer
23 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 ...
1
vote
1answer
60 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 ...
2
votes
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 ...