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
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
91 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
9 views

By doing appropriate calculations, explain why it would be inefficient to transmit electrical energy

By doing appropriate calculations, explain why it would be inefficient to transmit electrical energy from a 12-vlt car battery to a 12-volt, 24-watt DC car headlight bulb along a long cable of ...
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0answers
19 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
56 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
61 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
23 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
103 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
30 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
34 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} ...
0
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1answer
54 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
44 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 ...
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4answers
73 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 ...
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0answers
48 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 ...
1
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1answer
32 views

Regarding gauss law differential form

I have a big issue regarding the equality of integrands in gauss law. Given the integral form we have that $$\oint_{\partial\Omega}\vec{E}\cdot\vec{dS}=\int_{\Omega}\nabla\cdot \vec{E}dV={1\over ...
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2answers
27 views

Algebra with proportionalities?

Do the rules of algebra apply when you’re working with proportionalities? For example, I know that $P \propto \rho$, where $P$ is pressure and $\rho$ is density, and $\rho \propto m$, where $m$ is ...
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2answers
69 views

Distance covered by a brick in $1$ second time interval

A brick is dropped from the roof of a tall building.After it has been falling for a few seconds ,it falls $40.0$ meters in a $1.00$-s time interval.What distance will it fall during the next ...
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0answers
38 views

The Gauss theorem and discontinuity formulas for layer potentials

I'm studying electrostatics. I have solved, rigorously, the potential problem of volumetric distribution (I have proved continuity, potential existence in a point of charge distribution, and the ...
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1answer
44 views

Convert magnetic flux density to degrees

I have a digital magnetometer (compass) which outputs the following: Magnetic flux density ranging $\pm1229\mu\text{T}$ on the X axis Magnetic flux density ranging $\pm1229\mu\text{T}$ on the Y axis ...
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1answer
49 views

System of vector differential equations

How to solve numerically this system of vector differential equations (along with its initial conditions) without using any physical trick (like the reduced mass $\mu=\frac{m_1m_2}{m_1+m_2}$): ...
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0answers
35 views

Center of mass of semi ellipsoid using ellipsoidal coordinates system

Can anyone please show me -step by step- how to calculate the center of mass of a semi ellipsoid using ellipsoidal coordinates system? this is the ellipsoid I'm talking about. I solved it using ...
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0answers
47 views

Existence and uniqueness of solution to Euler rotational dynamics equations

In rotational dynamics the Newton-Euler equations express the dependence of angular velocity $\boldsymbol{\omega}$ of a rigid body from the torque $\boldsymbol{\tau}_{cm}$ with respect to the centre ...
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2answers
1k views

Xmas Greeting 2015

Simplify the expression below into a seasonal greeting using commonly-used symbols in commonly-used formulas in maths and physics. Colours are purely ornamental! $$\large \begin{align} \frac{ ...
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3answers
46 views

Why the average of the velocity is simply the average of the velocities when acceleration is constant?

I am studying physics equations for constant acceleration and I am having quite a hard time understanding the following. The average velocity is given by definition as $v_{av-x}=\cfrac{x-x_0}{t-0}$ ...
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0answers
36 views

How define the entropy of heat equation?

Today, I report a paper about Ricci flow, I saw entropy. As I know, entropy is a physical term.And I know it is used to describe how far the system from heat death.But I don't know the equation of ...
2
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1answer
29 views

Coordinate-free expression of a rotation

I'm interested in coordinate free (non-matrix based) approaches to geometry. What I'd like to do is to show that every Galilean transformation can be written uniquely as the composition of a ...
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2answers
62 views

Leaping frog algorithm

I need your help with a riddle, I need to find the best algorithm to catch a frog, The frog is on the Natural numbers, it begins at point L, each time it goes K Leaps right (means if it was at point ...
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3answers
39 views

Integrate $dx$ over interval $a\le x \le b$ instead of just $b-a$

In the Wikipedia article on the wave function it's stated that the probability of a spin-less particle in 1D space being found in the interval $a\le x \le b$ at time $t$, where $x$ is the position, ...
2
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1answer
55 views

Integral for Biot-Savart

What strategy is the quickest for solving the following integral? Note: this integral is generated by the need to determine the magnetic field at a point along the z-axis generated by a wire of length ...
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0answers
10 views

Convergence of a Double Summation solution to Laplace's Equation

For a cube of side length $a$ with 2 opposite sides held at the same potential $V$, the potential at the center of the cube can be expressed in series form as And I am trying to show that this ...
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0answers
53 views

How can we describe the diffusion of “things” injected into a fluid?

Let $d\in\left\{2,3\right\}$ and $\Omega_t$ be the bounded set occupied by a fluid at time $t\ge 0$. Let $c\in\Omega_0$ be a particle and $$[0,\infty)\to\mathbb R^d\;,\;\;\;t\mapsto ...
3
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1answer
32 views

Decide if a stack of overhanging blocks is stable

Suppose I have overhand blocks $1,2,3$ up to $n$ units long, one of each kind. They are stacked over the table from smallest to largest so that their left edge alligns. Show if it is stable. ...
2
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2answers
76 views

Elastic Strings and Simple Harmonic Motion

The Ceiling of a hall is 15m above the floor. A vertical elastic string of natural length 5m and modulus of elasticity 6N has one end attached to the ceiling and the other end attached to the ...
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0answers
145 views

Find the terminal velocity of skydiver using differential equations

I am studying differential equations in university and I came across this problem: A parachutist whose mass is $75$ kg drops from a helicopter hovering $4000\hbox{m}$ above the ground and falls ...
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1answer
37 views

Non-Constant Acceleration

How do we calculate time that we need for specific distance if we have non-constant acceleration. I have some formulas for other variable but don't have for time: Speed at time: $$ v(t) = ...
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2answers
42 views

Issues calculating double intergral

Calculate $$\iint_\Omega(x^2+y^2)^b\,dxdy$$ where $\Omega=\{(x,y)\in\mathbb R^2\,:\, x^2+y^2<a^2\}$ and $b>0$ is a real constant. I'm having trouble calculating the following, it's from a ...
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1answer
23 views

Limits and rate of change

I'm a freshman taking calculus 1 currently studying for finals. I am reviewing stuff from the beginning of the semester,and I don't remember the proper way to deal with limits like this one. A ball ...
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1answer
61 views

How can we describe the evolution of a density “injected” into an incompressible Newtonian fluid?

Let $d\in\left\{2,3\right\}$ and $\Omega\subseteq\mathbb R^d$ be a bounded domain. The evolution up to time $T>0$ of an incompressible Newtonian fluid with uniform density $\rho_0$ and viscosity ...
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2answers
42 views

Prove that if a particle travels a unit of distance in one unit of time starting and finishing in repose it has in a moment an acceleration $\ge 4$

How would you solve this problem? Prove that if a particle travels a unit of distance in one unit of time starting and ending whith velocity $0$ it has in a moment an acceleration $\ge 4$ (positive ...
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1answer
25 views

Find the starting height from which a particle projected horizontally at $40$m/s travels $100$m [closed]

This question is in my homework: A particle is projected horizontally with speed 40m/s from a point A. It hits the ground 100m horizontally from A. Find the height of A. Would it be possible for ...
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0answers
83 views

Implementation of a simulation of an incompressible Newtonian fluid with uniform density

Let $d\in\left\{2,3\right\}$ and $\Omega\subseteq\mathbb R^d$ be a bounded domain. I want to simulate an incompressible Newtonian fluid with uniform density $\rho$ and viscosity $\nu$. The evolution ...
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0answers
16 views

Drawing a diagram to determine force from the cross product

I've been having some trouble drawing a diagram for the torque produced by a magnetic field on an n turn rectangle in the xy plane about the y axis and wanted to make sure that my diagram is indeed ...
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0answers
21 views

Why can lorentz transformation be expressed like this

Why can the lorentz transformation: https://upload.wikimedia.org/math/e/3/e/e3ee37f49f0adb02bc81590cb697d4d0.png Also be expressed as ...
2
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1answer
67 views

Applied Mathematics: Spherical Polar Coordinates and Newton's Second Law

I've been attempting this question but can't seem to find a solution. Question: A particle of mass $m$ moves under the influence of a force which, in spherical polar coordinates, only acts in the ...
2
votes
1answer
78 views

What exactly is Green's Function and why can I use it to solve harmonic oscillator problems?

My question: What exactly is Green's Function and why can I use it to solve harmonic oscillator problems? In other words, how is Green's function connected to physics problems like the ...