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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What kinds of motion obeys a higher order form of angular motion?

Angular velocity $\vec{\omega}$ can be defined in terms of velocity $\vec{v}$ and position $\vec{s}$ as: $$ \vec{\omega} = \frac{\vec{s} \times \vec{v}}{\left\lvert s\right\rvert^2} $$ Constant ...
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0answers
29 views

Show a beam is in equilibrium given the stress tensor

Having some trouble with this: https://gyazo.com/0835bdaa8e01cb976765aac94555f6ef I know how to show that at x_2 = -h the surface traction is zero, but I'm not sure how to show it's in equilibrium? ...
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1answer
92 views

Integrate second order DE once

Given the vorticity equation $$\frac{D \omega}{Dt}=(\omega \cdot \nabla)\textbf{u}+ν\nabla^2ω$$ and $\textbf{u} = (−αr/2,v(r),αz) $ in cylindrical polars where alpha is positive constant. Find $\...
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0answers
35 views

About periodic trajectories of a Hamiltonian system

Consider a Hamiltonian system with Hamiltoniana $H (\mathbf{q}, \mathbf{p})$, where $H$ doesn't depend on time $t$. It is known that in some domain of phase space the trajectory of system are peiodic. ...
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3answers
273 views

What is the moment of inertia of a Gosper island?

We know that regular hexagons can tile the plane but not in a self-similar fashion. However we can construct a fractal known as a Gosper island, that has the same area as the hexagon but has the ...
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1answer
16 views

Velocity along curve given velocity in one axis

Let's say that I have some particle travelling along a 2D trajectory mapped out by some infinitely differentiable function $f$ (in this case $f(x) = x^{-1}$). I know the velocity of the particle ...
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0answers
37 views

(Differential Galois Theory) Where is the proof that the three-body-problem is unsolvable?

I'm looking for a proof, which shows that "the 3-body-problem" in physics is mathematically unsolvable. Does anyone know some URLs that contain a proof in mathematical detail? You know, in ...
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1answer
13 views

Finding the radius of frustum cone?

I'm trying to understand how can i find the radius from the figure , the solution of the radius is given in the equation but I'm not getting how its derived enter image description here
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1answer
53 views

Finding the distance between two moving objects

In this case there is a missile whose initial position is $A(30,40)$ with a velocity of $[50,30]$ and an asteroid whose initial position is $B(400,250)$ with a velocity of $[-20,-30]$. The position of ...
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2answers
60 views

Circuit Analysis problem (find the problem)

In this question, I know that $\text{C},\text{R},\text{T},\text{A}\in\mathbb{R}^+$ I've this circuit (the bottom of the resitor is connected to earth ($0$)): When I use Laplace transform I can find ...
2
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2answers
43 views

Second order non linear differential equation: Central force question

The problem is as below: I have derived that the particle satisfies the motion equation $$ \frac{d^2u}{d \theta ^2 } + u = \frac{F(1/u)}{mh^2u^2} $$ by Newton's Law, $u= 1/r$ and $h = r^2 \frac{d \...
2
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1answer
30 views

Unique ground state of Schrödinger Operators

I'm reading a book and there is an argument that the ground state of a Schrödinger operator is unique. The problem is I think the argument is complete non-sense! These are lecture notes by Witten, I ...
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2answers
18 views

If the height of an upwardly thrown ball can be approximated by $h(t)=h_0+v_0t-\frac{g}{2}t^2$, what is $\frac{h(t_2)-h(t_1)}{t_2-t_1}$ conceptually?

I know that it describes the secant through $(t_1,h(t_1))$ and $(t_2,h(t_2))$, but I wouldn't know how to interpret it in "real life" terms. I also know that if $t_1$ tends towards $t_2$, I get the ...
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1answer
84 views

Employing Newton's Laws with differential equations [closed]

Going through some problem sheets from previous semesters and can't find a full solution for this question so was wondering what the answers might be. A particle of mass $m$ moves on the $x$ axis ...
3
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0answers
29 views

Dissipation term in wave equation

If we're given a string with mass density $\rho$ in units $\frac{M}{L^3}$ with constant cross-section $A$, tension $T$ in units $\frac{F}{L^2}$, and whose length is $L$; and then we assume that the ...
2
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1answer
46 views

Ellipsoid moment of inertia matrix

Some background info: torque $\tau$ is defined as $$\tau = I*d\omega$$ Where $I$ is the moment of inertia matrix and $d\omega$ is an object's rotational acceleration. As I understand it, the inertia ...
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1answer
28 views

Calculate position with increasing acceleration.

So if calculating the change in an object's position (with a constant acceleration) is done with this equation: $o = vt + (\frac12)a t^2$ $o$ is offset from original position $v$ is starting ...
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1answer
65 views

Parabolic slide

Given a friction-less slide $y=x^2$, place a particle on the slide at $(1,1)$. The particle is acted upon by constant gravity $g= 9.8$ units/s/s. At what time does it reach bottom? The ...
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0answers
14 views

Modeling population density with PDE

If we know that the population density $u(x,t)$ in some lake varies as a function of $x>0$ and time $t$, where $x$ increases downwards with depth, and that the population diffuses with constant $D$ ...
2
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1answer
33 views

Vector Force Application

I have this question for Math StackExchange Site. Suppose you would like to cros a $132 ft$ -wide river in a motor boat. Assume that the motorboat can travel at $7.0mph$ relative to the water and ...
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0answers
21 views

Writing PDE in the form of convervation law

What does one need to know in order to write $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+\frac{\partial^3 u}{\partial x^3}=0$ in the form of a conservation law, which contains the ...
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0answers
46 views

Why don't more celestial bodies exhibit higher-order rotations?

It is well known that the Earth spins on its axis. It is also well known that the Earth's axis also precesses, i.e. spins around a secondary axis, much more slowly. Less well known is that we have ...
2
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1answer
22 views

Computate the commutator $[p^n,x]=-ihnp^{n-1}$

Computate the commutator of $[p^n,x]=-ihnp^{n-1}$. With $p=-ih \frac{\delta}{\delta x}$ the impulse operator. $h$ stands for $\frac{h}{2\pi}$. Answer: I do it with induction over $n$. For $n=1$ it ...
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2answers
33 views

Two trains and a fly using the series

I'm having some difficulties dealing with this problem: A train starts travelling from A towards B. It's velocity is v. Simultaneously train starts travelling at the same velocity from B to A. The ...
2
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1answer
45 views

Pendulum loss/gain of time per day given : $\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$ and max displacement $5^{\angle}$

Here is what i am given: The oscillations of a pendulum are described by the equation: $$\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$$ where $\phi$ is the angle between the pendulum and the vertical axis, $l$...
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0answers
91 views

A version of Ampère's law

The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law uses the fact that, if $\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3$, $\boldsymbol{J}\in C_c^2(\...
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1answer
38 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
43 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
votes
1answer
15 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
15 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
37 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
16 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
20 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
30 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
41 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 ...
1
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1answer
27 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
91 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
38 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 ...
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1answer
30 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
433 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
21 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 ...
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1answer
31 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
40 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 ...