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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128 views

How do I use the integral of work to solve the circular pool problem?

I am in Calculus 2 and ran across this problem. I'm struggling with this subject in general, so I suspect I may be missing something fairly fundamental. A circular swimming pool has a diameter of 14 ...
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0answers
50 views

Runge-Kutta 4 in polar coordinates

How is the Runge-Kutta method implemented on this differential equation: $$ \frac{d^2 \theta}{dt} = -\frac{g}{l} \theta $$ (pendulum motion) which is in polar coordinates? Let: $c = \frac{g}{l}$ ...
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2answers
42 views

Help with Differential equation solution requried

Hi guys I am doing some differential equations and I got this one: I have no idea how he went from (38) to (39). When I solve it by integrating factor, the equation I have is: ...
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1answer
47 views

Velocity Verlet method: How to calculate acceleration

The velocity Verlet method algorithm is as follows: Calculate: $$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t)\, \Delta t+\tfrac12 \,\vec{a}(t)\,\Delta t^2$$ Derive: $\vec{a}(t + \Delta t)$ from ...
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0answers
23 views

Calculating the sun position fails

could you help me find the mistake(s) in my calculation of the sun position today on hawaii at 16:00? I'm following this Wikipedia article. Number of days since 2000/01/01 (2016/01/29): $$n ...
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2answers
499 views

Mathematical meaning of certain integrals in physics

While studying on texts of physics I notice that differentiation under the integral sign is usually introduced without any comment on the conditions permitting to do so. In that case, I take care of ...
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0answers
49 views

Understanding derivative notation in those equations

I am given the following set of equations from a physics course, which is about longitudinal waves in rods. My questions are: On the second line you have $ (\frac{\partial \Delta}{\partial x})dx ...
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1answer
44 views

Understanding projectile motion formula with air resistance

$\frac{dx}{dt} = v_x$ $\frac{dy}{dt} = v_y$ $\frac{dv_x}{dt} = -b|v|v_x$ $\frac{dv_y}{dt} = -g -b|v|v_y$ where $v = \sqrt{v^2_x+v^2_y}$ and $b$ is a drag constant Why is it that the magnitude of ...
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0answers
35 views

Simple Harmonic Motion; Tension in Elastic rope

I'm struggling to model this question out correctly. A glider and its pilot have total mass $230$ kg. The glider lands on a horizontal airstrip and when its speed is $16$ m/s it hooks on to the ...
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2answers
44 views

Problem about curves. A particle is running along circumference $x^2+y^2=25$

I'm considering a problem about curves. A particle is running along circumference $$x^2+y^2=25$$ with a costant modulus speed compliting a turn in 2 second. I need to determinate the acceleration in ...
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4answers
57 views

Proving $s = ut + \frac{1}{2} at^2 $

I have been asked to prove on a graph that $s = ut + \dfrac{1}{2} at^2 $ I know that the area of the rectangle is $ut$ but the area under the triangle is $\frac{1}{2}\times t \times (v-u)$ So ...
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2answers
168 views

Dirac's delta in 3 dimensions: proof of $\nabla^2(\|\boldsymbol{x}-\boldsymbol{x}_0\|^{-1})=-4\pi\delta(\boldsymbol{x}-\boldsymbol{x}_0)$

If $T_f$ is a distribution, i.e. a linear functional, continuous according to the convergence defined here, defined on the space $K$ of the functions of class $C^\infty$ that are null outside a ...
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1answer
22 views

velocity with height of time for an arbitrary projectile being launched from a cliff

I have a question about an arbitrary projectile being launched and an arbitrary polynomial describing the height(time) = h(t). The question goes onto ask about the velocity at different points in ...
3
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1answer
67 views

Momentum is quantised in compact spaces?

Background One of the first examples given when studying quantum mechanics is the particle on a cylinder, or particle on a ring. One finds that because of the periodic boundary conditions, ...
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1answer
71 views

How does angular acceleration change with revolutions?

So, for a section of my EPQ (A-Level, Extended Project Qualification), I am trying to analyse a hypothetical circular accelerator using the angular motion equations for constant angular acceleration. ...
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0answers
46 views

What's so special about involute curves??

An involute curve (specifically, an involute of a circle) is very commonly used to define the shape of the teeth on a gear. Apparently this idea goes back to Euler. Why is this? What special ...
2
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1answer
36 views

what is the relation between the Physics Density and the Topological Density

A relation between both is that both deal with how accumulate is something (the notion of density per se), however, I was wondering if there is any "math" relation between both? Thanks
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0answers
13 views

Reference request: 2D conformal field theory and the honeycomb lattice

Would anyone know what is meant by "conformally invariant" functions defined on the plaquettes of the honeycomb lattice (ie the function is defined on the vertices of the dual tringular lattice)? ...
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1answer
30 views

How to calculate angle between two objects in orbit

So I have 2 objects in orbit around the same body, and I have all the orbital elements associated with each body. How do I calculate the angle between them both or figure out when they are a certain ...
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0answers
44 views

What's the name of this problem? Interesting minimisation of a length.

There is a problem which has to do with minimising the length of a (possibly disjoint) barrier in a region of space (often a 2D circle) such that no straight line can pass through the particular ...
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2answers
49 views

Noob doubt about signs in equations

I wanted to solve some simple free fall with friction models so I wrote (with $x$ axis orientated down for convenience) $$m\ddot x=mg -k\dot x$$ which I turned in $$m\dot v=mg -kv$$ with $m,g,k$ ...
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1answer
35 views

Show, for a sphere, $\langle r^2\rangle = \frac{3}{5}r_o ^2$

The following equation is used as an inference but not explained in my solid state physics book (Economou, "The Physics of Solids"). I figure it's a math/geometry problem so I ask here. Can anyone ...
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1answer
68 views

Maths And Technology: calculating angles of mirrors for a laser.

HELP// maths and technology(light) hello! So, I have a class project in which we have to secure a piece of art in a 'museum'. In this project we have to use a laser, 2 mirrors and a sensor (basic ...
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1answer
18 views

Can I replot a model with an extra axis while saying the exact same thing?

I asked a poorly received question on physics stack exchange, about the universe. Today I left the comment: can we imagine the universe "expanding into nothingness" if we're clear that ...
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1answer
34 views

Rewrite a Lagrange function to Euler-Lagrange equation in polar coordinate

If we have a Lagrange function in the form $L(p, q) = \frac{p^2}{2} + q^2$, how could it be re-written as a form of Euler-Lagrange equation in polar coordinates ?
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1answer
28 views

Ski simulation - Velocity vector components

So I am creating a physics ski simulation as a project on my University and the task that I've been struggling with for a couple of hours is: How fast is a Skier moving towards a still obstacle at ...
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1answer
34 views

Average Velocity over a time interval

A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation $x(t)= αt^2− βt^3$, where$ α = 1.45 m/s^2$ and $β = 0.055 m/s^3$ ...
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2answers
231 views

Finding the Centroid of a segment

I am having some confusion about the following. As I had never done much physics, this is the first time I have came across the topic. I am asked to find the centroid of the disk segment $x^{2}+y^{2} ...
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0answers
31 views

Conversion of polar equations when you change the position of the origin

I'm working on a physics problem that is described as follows: "I am standing on the ground beside a perfectly flat horizontal turntable, rotating with constant angular velocity w. I lean over and ...
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0answers
42 views

Controlling a flying vehicle with multiple thrusters

I'm working on a problem involving a vehicle with $n$ rocket engines, as seen here: The task is, given the desired force $\vec F$ and torque $\vec \tau$, calculate the optimal thrust for each ...
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2answers
159 views

phys questions referring vectors

Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces A⃗ , B⃗ , and C⃗ shown in the figure below Find the magnitude of a fourth force on the stone that ...
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0answers
48 views

Calculate the resistance between 2 adjacent nodes on a shape using graph theory

In shapes like regular octahedron or dodecahedron, how can Graph Theory be used to calculate the resistance between two adjacent vertices? All edges are assumed to have unit resistance. Is there ...
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1answer
31 views

Suppose that you measure three independent variables as…

Suppose that you measure three independent variables as $x = 6.5 \pm 0.8; y = 3.1 \pm 0.3; \theta = 40^\circ \pm 3^\circ $ and use these vales to compute $$q = \frac{x^2 + y\sin\theta + 2}{x + ...
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2answers
92 views

Problem with differential equation RLC circuit series

I am trying solve the differential equation of RLC's circuit in series, I have: $C=4\ F, L= 1\ H$, $R=5\ \Omega$, and $V_e=20\ V$. $1)$ first I got the equation, it is: $i''+5i'+\frac{1}{4}i=0$, what ...
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0answers
21 views

Backwards Euler for gravitational equation

I have a set of ODEs that simulates a body that moves. Let's say a meteor falling towards the sun. Implementing the explicit Euler is easy $\vec{d}_{n+1} = \vec{d}_n + \Delta t\vec{v}_n$ ...
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2answers
67 views

Position vector of a particle moving with constant speed on a straight line

Suppose we have a particle which starts from a point $A$ and moves with constant speed $u$ along the line $AB$. One wants to show that the position vector $\mathbf{x}$ of the particle at time $t$ is ...
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1answer
43 views

Coherent states - operator algebra problem with physics motivation

Motivation: I have a mathematical problem motivated by quantum field theory in physics. It should be quite easy to prove, but for some reason I can't do it. Intro: Let there be operators $\hat{a_i}$ ...
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0answers
62 views

How To Prove The following equation?

The equation arised in the paper:Exact and asympototic representations of the sound field in a stratified ocean.That is the equation(3.12) for solving the problem $$\Delta ...
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1answer
26 views

analytical hard sphere collision condition with periodic boundary conditions

Hello Stack Exchange Mathematics, I am curious if there is an analytical or efficient numerical solution for the collision of hard spheres in a rectangular unit cell with periodic boundary ...
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2answers
105 views

Integral of an unbounded function as a solution of $\nabla^2\boldsymbol{A}=-\boldsymbol{J}$

While studying the equivalence between the Biot-Savart and Ampère's laws I have only found proofs of the fact that$$\boldsymbol{A}(\boldsymbol{x})=\frac{\mu_0}{4\pi}\int_V ...
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0answers
41 views

Solution to the Schrödinger equation

Let $$\begin{cases} i\frac{\partial}{\partial t} \Psi(x,t) = \Delta \Psi(x,t);\\ \Psi(x,0) = \varphi(x) \end{cases}$$ Why do physicists seek a solution of this equation in the form: $$ \Psi(x,t) = ...
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3answers
81 views

What is the force acting on an object inside a spaceship?

A $7.5$ kg instrument is hanging by a vertical wire inside a spaceship that is blasting off from rest at the earth's surface. This spaceship reaches an altitude of $208 $m in $20$ s with constant ...
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1answer
30 views

Need to solve for t but can not work out how to get t on one side

I have a object in free fall with $g$ = acceleration, $y$ is the position above the ground and $t$ = time. I worked out that to find the speed at and $t$ is $dy = g . t$ So to get the position $py$ ...
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1answer
31 views

Mathematical physics - Expand the a series of binomial [closed]

Expand the a series of binomial $\left(1-\frac{v^2}{c^2}\right)^{-\frac{1}{2}}$. Enter the first three terms. What is the ratio of third term to second if $\frac{v}{c}=0,1$?
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0answers
37 views

Fokker-Planck derivation. Path integral?

I am trying to understand the development of Fokker-Planck equation as is described here. Unfortunately, I cannot understand how the first equation on page 4, \begin{multline} \frac{1}{2} ...
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1answer
55 views

Getting started on Celestial Mechanics

I am searching for a math-accurate book on this subject, in particular for this topics: $n$-body problem, getting more detailed when $n=2$. Efeméride calculation. Orbit determination. Perturbation ...
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1answer
45 views

Why are these triangles similar ? (Derivation of uniform circular motion equation )

I am studying the equations of uniform circular motion and I am having difficulties with the derivation of them. I quote my book : We can find a simple expressio for the magnitude of the ...
2
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4answers
77 views

Using polar coordinates to find the area of an ellipse

Considering an ellipse with the $x$ radius equal to $a$ and the $y$ radius equal to b$:$ I figured that some kind of parameterization might be: $x=a\cos\theta$ $y=b\sin\theta$ and then polar ...
2
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0answers
52 views

Gauss´s law proof “details”

I know that this question has already been asked multiple times but I´m still not getting on the mathematical details behind the answers... So I hope that this question doesn´t get closed; also I ...
4
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2answers
59 views

Understading the integral form of a conservation law

When I think of a conservation law I think of a continuity equation like the following $$\partial_t \rho = -\nabla \cdot \vec j$$ But now I'm reading a book on electrodynamics (that's honestly a bit ...