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
13 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
30 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
180 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
29 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
34 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
95 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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40 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
23 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
80 views

Problem with differential equation RLC circuit serie

I am trying solve the differential equation of RLC's circuit in serie, 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
18 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
36 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
35 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
60 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
18 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 ...
4
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1answer
69 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
36 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
66 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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29 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
48 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
36 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
68 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
47 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 ...
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2answers
52 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 ...
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1answer
27 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
49 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
31 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
40 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
47 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
26 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
44 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
45 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
31 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
28 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
57 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
45 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
9 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
50 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
29 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. ...
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2answers
54 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 ...
2
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0answers
83 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
36 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
40 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
19 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
59 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 ...