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
29 views

What direction would a hinge's reaction force point?

In my homework question there is a ladder with the bottom touching the smooth floor and the other end is attached to a hinge. I need to draw a force diagram and use that to find the normal. There is ...
2
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1answer
41 views

Vortex flow - Surface Integral

Consider the vortex flow of a fluid of density $\rho$ where the fluid rotates with an angular velocity $\omega$ about the $z$-axis. Determine where a unit square $S$ on the $yz$-plane should be placed ...
2
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1answer
13 views

Dipole-Coupling Tensor: Electrostatic Dipole Moments

I've been struggling with this problem today. Here's an image of the question I'm attempting to answer. I'm relatively new to tensor algebra (I've been studying it for about a week or two), and I've ...
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2answers
14 views

Calculating quantities with regards to a pendulum

The set up is a pendulum of length 2m with a mass on the end at 0.5kg. The mass is released at a small initial angle of 6 degrees moving into harmonic motion. I need to calculate the angular ...
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1answer
36 views

two dimensional heat equation

Please I really need some help for this exercise, I can't solve it for any ways... I need to prove the maximum principle for the two dimensional heat equation with zero boundary data. Really I need ...
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0answers
14 views

Error propagation in complex formula

I'm currently trying to use error propagation formulae to calculate an estimate for the error in the following molecular dynamics formula: $C_v^* = \frac{3}{2}\bigg[1-\frac{2}{3NT^{*2}}\big\langle (\...
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1answer
19 views

calculate the speed of a ball, with a laser

I'm doing a project where I have to calculate the speed of a ball, passing a certain point. I want to do this with a laser, by taking the time the laser is broken in comparison of the ball it's size. ...
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0answers
29 views

Approaching a Trajectory Problem

I am trying to design a railgun simulation. The idea is that the user can supply a starting point and velocity vector for a launcher and for a target, and the launcher will find the angle to launch ...
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0answers
31 views

Heat problem with an internal source of heat for which the maximum principle doesn't hold.

Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it... $$u_{t}=u_{tt}+2(t+1)+x(1-x) , 0&...
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0answers
39 views

$\frac{\omega}{2\pi}\int_0^{\frac{2\pi}{\omega}}\frac{\sin^2\theta \cos^2\omega t}{(1+\beta\cos\theta \sin\omega t)^5} dt$

I'm going to write out the whole problem as it is given to me (bad grammar and all) even though some of the info may be irrelevant to finding a solution. A charge $e$ moving along a straight line ...
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0answers
47 views

Uniform current in cylinder and straight wire causing same magnetic field?

The tridimensional version of the Biot-Savart law says that the magnetic field generated at the point $\boldsymbol{r}\in\mathbb{R}^3$ by a tridimensional distribution of current defined by the current ...
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1answer
26 views

finding curvature radius

given a projectory equation of the form $ y=y(x) $find the curvature radius as a function of $x.$ a projectory equation , hence $ x=x(t)$, input that in y and we get $y=y(x(t))$, which is what one ...
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1answer
69 views

Instantaneously at Rest. What does it mean?

What is instantaneously at rest? Does it mean that velocity and acceleration must be both 0? So for question, $v(t) = 3 - t/2$, $t>4$, why is $t=6$ instantaneously at rest?
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0answers
36 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
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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 value of $...
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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 ...
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3answers
432 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 $\left(\frac{\text{d}}{\text{d}...
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0answers
20 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, ...
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2answers
32 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 ...
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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
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1answer
28 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. ...
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0answers
40 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 $...
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0answers
36 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 infinite-...
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3answers
38 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 ...
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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 ...
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1answer
35 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 ...
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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
16 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
30 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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0answers
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
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} ...
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1answer
34 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
17 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) ...
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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
26 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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0answers
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". ...
5
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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
39 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
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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
34 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
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1answer
28 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
41 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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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
26 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 ...
4
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1answer
54 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
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1answer
114 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 ...