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Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.

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What is the fault in this method of finding second moment of area of a circle

I am trying to find the second moment of area of a circle about a diameter using first principles. Place the centre of the circle at the origin of XY-plane. Now consider a tiny circular sector with an ...
Jarvis's user avatar
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0 answers
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Some details concerning projective representations in Wienberg's book

I have a question from the book "the quantum theory of fields" by S. Weinberg in page 89: How can we get $[U(\Lambda )U(\bar{\Lambda})U^{-1}(\Lambda \bar{\Lambda})]^2=1$ from the fact that ...
Mahtab's user avatar
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28 views

Solving challenging 4D integrals arising from triangle-triangle gravitational interaction

I am trying to find a closed form for two related integrals, coming from a physics problem partially solved here, about attractive forces between two triangles : $$\begin{align} {\bf F}_1 &= -G ...
user1420303's user avatar
-3 votes
0 answers
31 views

A reference for Lie groups as groups of transformations of a target space

I would really appreciate if someone could introduce me a reference for studying Lie groups as groups of transformations of a target space. Thanks in advance.
Mahtab's user avatar
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Spinors on (euclidean signature) spacetime

Let's consider a spacetime $M$ which is a also spin manifold. In Euclidean signature We have that the frame bundle is a principal $GL(4,\mathbb{R})$ bundle over $M$. Even dimensional spin manifolds ...
R. Rankin's user avatar
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How to expand $(D_\mu\Phi)^\dagger(D^\mu\Phi)$ in $SU(2)$

I would like to calculate the following expression: $(D_\mu\Phi)^\dagger(D^\mu\Phi)$ where $D_\mu\Phi = (\partial_\mu-\frac{ig}{2}\tau^aA_\mu^a)\Phi$ and $A_\mu^a$ are the components of a real $SU(2)$ ...
Hendriksdf5's user avatar
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0 answers
32 views

Calculate optimal spacing for magnetic field measurement using Gaussian Multivariate likelihood distribution

I posted this question on Physics exchange as well, but is rather mathematic :) I have a vertical magnetometer configuration, and measure lines on the ground. I want to calculate the optimal spacing, ...
user387449's user avatar
3 votes
2 answers
60 views

How to interpret the condition of a circumference rolling without slipping on another circumference

Suppose a circumference of radius r and center $\Omega$ rotates with constant angular velocity $\omega_D=\dot\phi e_3$ (D stands for disk) around an axis parallel to $e_3$ through $\Omega$. Let $\...
Davide Masi's user avatar
1 vote
0 answers
43 views

Scaling and Helmholtz equation

Solutions to Laplace equation and powers thereof have some convenient invariance properties that solutions to Helmholtz equation $\Delta u-u=f$ apparently lacks, especially in regards to scaling, ...
undefined's user avatar
  • 277
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1 answer
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Galileo transformation group

I am reading the book "Mechanics" by Florian Scheck, more specifically on Galileo's transformations. The author states, in paragraph 1.13 if anyone has the text, that the more general ...
Nameless's user avatar
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1 answer
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Calculate azimuth and pitch angle from total angle and direction

I am looking for a way to compute the azimuth and pitch angles from a system where I only know the total angle and I know the circular direction of the angle. Let $a =$ azimuth angle and $b =$ pitch ...
tyobrien's user avatar
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On-Axis Magnetic Field of a Finite Continuous Solenoid

I am attempting to verify the equation for the magnetic field on axis of a finite continuous solenoid posted to this wikipedia page. The equation is $$ B_z = \frac{\mu_0 NI}{2} \left( \frac{\frac{l}{2}...
Bunji's user avatar
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-2 votes
1 answer
48 views

Magnitude of Instantaneous Velocity $=$ Instantaneous Speed Rigorous Proof [closed]

In physics, for an infinitesimal time period $\lvert dr \rvert = ds $ Where $dr$ is displacement and $ds$ is the distance covered. I understand this idea intuitively but am eager to know a rigorous ...
GameTime With Aryan's user avatar
0 votes
0 answers
22 views

Finding the optimal surface enclosing a given volume

I would like to find, over the set of continuous surfaces that enclose a volume $V$, the one(s) that lead to the maximal value of a certain cost function. I'm working on a physics problem which ...
amrit 's user avatar
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1 answer
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How to solve this equation analytically

when considering the problem of solving how much mass of fuel does a rocket need in order to leave earth, we come across this equation: $$ v_{\infty}=-\frac{g}{Q}m_c+u\ln(1+\frac{m_c}{m_f}) $$ Where $...
realreal's user avatar
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-1 votes
1 answer
65 views

I want a formal mathematical definition of the configuration space of a system (mathematically defined examples appreciated)

The Wikipedia article on configuration space offers this "formal definition": In classical mechanics, the configuration of a system refers to the position of all constituent point particles ...
Nate's user avatar
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How to accurately average a function with a nonlinear response?

I am a physics PhD student working in optics and I have a bit of a weird problem that I am trying to sort out and I'm hoping you math folks can help me with. Without boring you with the experimental ...
UltrashortGiraffe's user avatar
6 votes
2 answers
93 views

Optimal length of rope for sliding across a gap

I'm trying to solve a physics problem that I heard ~10 years ago in undergrad that was casually posed to me without a solution in mind; it has been bothering me ever since! Please let me know if this ...
pretzelKn0t's user avatar
1 vote
1 answer
55 views

A PDE problem: heat eqaution with variables separation method

I have to solve a PDE problem called "Heat equation": $ \begin{cases} u_t = a^2u_{xx}+2xt,0<x<1, t>0 \\ u_x(0,t)=-1, u(1,t)=t \\ u(x,0) = 1-x-\cos(\frac{7\pi}{2}x) \end{cases} $ I ...
Zola's user avatar
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1 vote
4 answers
104 views

How does the solution make sense for this ODE about distance and time?

I have an equation: $$ \frac{d^2x}{dt^2} = \left(\frac{dx}{dt}\right)^2 + 1 $$ where x and t represent distance and time respectively for $\frac{dx}{dt} = 0$ and $x = 0$ when $t = 0$ After solving ...
BadUsername's user avatar
1 vote
1 answer
68 views

Calculating deflection on a beam

This is for a hobby project, and to learn a little about elasticity along the way. I have a triangle wedge comb piece of decreasing width and angle for which the cross section is shown here: For each ...
vallev's user avatar
  • 396
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0 answers
23 views

Tackling the 2-D Continuity Equation with a dependent source term

I am modeling what is effectively a conducting plate in (spatial variables $x,y$) which the charge density $\rho$ satisfies the continuity equation with current density $\mathbf{J}$. Because I am ...
bfrost97's user avatar
3 votes
1 answer
175 views

Understanding Newtonian mechanics using concepts from differential geometry

In a book I'm reading (Friedrich and Agricola), I encountered the following definition of a "Newtonian system": An autonomous Newtonian system is a triple ($M^m$, $g$, $X$) consiting of a ...
guibor's user avatar
  • 135
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0 answers
30 views

Help with Proof of Perron-Frobenius theorem in "Mathematics and Physics of Many Body systems"

In the book Mathematics and Physics of Many Body systems by Hal Tasaki, he gives a proof of a version of the Perron-Frobenius theorem (see below). However I don't follow the line in (2) Since $u_i m_{...
JvT's user avatar
  • 56
0 votes
3 answers
99 views

Physics Kinematics Equation Derivation

I was wondering how you can derive the physics kinematics equation $\Delta x = v_f\Delta t - \frac 12 a \Delta t ^2$ algebraically. I understand where this equation comes from geometrically (when a=...
BakedPotato66's user avatar
0 votes
0 answers
42 views

Boundary conditions of partial differential equations.

I have a question about the boundary conditions of partial differential equations. Suppose we want to solve the equation $$ \mathcal {L}u = f \ \text{in} \ \Omega $$ $$ u = g \ \text{on} \ \partial \...
topst's user avatar
  • 149
2 votes
3 answers
82 views

How to compute the volume integral for the potential of an arbitrary point outside a uniformly charged ball?

$$\frac{\rho}{4\pi\epsilon_0}\iiint_{D}^{}\frac{1}{\left\| \mathbf{r}-\mathbf{r'} \right \| }dV'$$ $D$ is a ball of radius $R$ $\mathbf{r}$ is the position vector of the point where we want to ...
giannisl9's user avatar
  • 163
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0 answers
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Is there a way to prove Pappus's Centroid Theorem (volume-related) using the area-related one?

I am curious about proving the Pappus's Centroid Theorem. I have finished proving the area one and I wonder if there is a way to intuitively prove the volume one by using the area one (we can view the ...
Stephanie Yao's user avatar
0 votes
1 answer
57 views

Target position given ship velocity and bullet velocity.

Let's say we have two ships. Both have a velocity and the first ship has a turret with autotargeting. For simplicity let's say the ship is a point and a bullet comes out of that point. The first ship ...
Vinny's user avatar
  • 15
0 votes
1 answer
32 views

How to verify positive definitiveness of the given Kinetic term?

I was going through this paper on QCD chaos, where in Appendix B (page 10), for equation B12: $$\frac{\mathcal{S}}{\mathcal{T}}= \int dt\sum _{n=0,1} \left(\dot{c}_n^2-c_n^2 \omega _n^2\right)+11.3c_0^...
codebpr's user avatar
  • 121
1 vote
0 answers
70 views

Does a generalization of the Sokhotski-Plemelj Formula to four (or higher) dimensions exist?

The Sokhotski-Plemelj Formula states \begin{equation} \frac{1}{x \pm \textbf i \eta} = \mathcal{P} \left(\frac1x\right) \mp \textbf i\pi \delta(x) \end{equation} where this expression has to be ...
Steven's user avatar
  • 11
-1 votes
1 answer
114 views

General relativity [closed]

I was reading a physic text, and I don’t understand how to transform their non rigorous argument. The part where I don’t get it is when they write $d\theta=d\phi=0$. It means nothing as $d\theta$ and $...
Maxime's user avatar
  • 319
0 votes
0 answers
35 views

Proof of Schur-Weyl duality

$\newcommand{\ket}[1]{|#1\rangle}$ I am reading an article (Joy Lie, 2019, "The Quantum Schur Transform and its Applications"), about the quantum Schur transform. There, it is stated that ...
CaLa's user avatar
  • 23
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0 answers
23 views

Diffraction cone visualization

I have a problem visualizing the diffraction cone for rays coming from different sides: Although I've read multiple papers on the topic, my math skills aren't strong enough to fully grasp it, as I'm ...
Etinne's user avatar
  • 1
1 vote
0 answers
44 views

Can this property that I formulated be used to find solutions to Navier Stokes in cylindrical coordinates?

Let's say I want to derive a vortex flow function $$\psi (r,t)$$ using a scalar field bell surface of the form below, where $W(t)$ controls the width (but is not actually the width) as a function of ...
Tayler Montgomery's user avatar
-1 votes
3 answers
53 views

How to untangle the ODE $\frac{dx}{dt} = c + \frac{px}{l_0 + pt}$? [closed]

In working on this problem, I came up with the following differential equation: $$ \frac{dx}{dt} = c + \frac{px}{l_0 + pt} $$ where $x$ is the dependent variable, $t$ the independent, and all others ...
SRobertJames's user avatar
  • 4,450
4 votes
0 answers
170 views

Dynamics of a sliding cube on the $XY$ and $YZ$ planes

A cube with side length $a$, is initially placed with one vertex at the origin, and its faces parallel to the coordinate planes ($XY, XZ, YZ$) and totally lying in the first octant. Then its rotated ...
Quadrics's user avatar
  • 24.3k
0 votes
0 answers
18 views

Series Solution of Laplace Equation in Spherical Coordinates

I am a physics student and this question was asked on the Physics stack exchange as well. I just want you to go through the derivation first. I was recently Studying Griffiths Electrodynamics after a ...
Charu _Bamble's user avatar
3 votes
1 answer
63 views

Mach equation algebraic manipulation

I'm trying to go from: $$ M^2 = \frac{M_S^2 + \frac{2}{\gamma-1}}{\frac{2M_S^2 \gamma}{\gamma-1} - 1}$$ to: $$ M^2 =1 - \left[\frac{\gamma +1}{2 \gamma} \right] \left[ \frac{M_S^2-1}{(M_S^2-1) + \frac{...
MicrosoftBruh's user avatar
0 votes
1 answer
66 views

Proof of a mathematical step involving trigonometric functions

On a scientific paper I found a strange step, from this ($\theta$ and $\phi$ are time-dependent; $\gamma$, $g$, and $l$ are constants): $$ \ddot{\theta} - \ddot{\phi} - \ddot{\theta} \, \cos(\phi) + \...
Federica Guidotti's user avatar
0 votes
0 answers
20 views

Alternative definition of ergodicity for physical systems

Imagine we have a physical system whose dynamics are given by its hamiltonian H, defined in a space A. My question is whether the following definition is equivalent to saying that the system is ...
VíctorBayona's user avatar
0 votes
0 answers
37 views

Inverse of a matrix sum and difference in terms of known inverses

I have been working on a problem related to the inverses of matrices and would appreciate any insights or solutions. The problem is as follows: Given two invertible matrices $A$ and $B$ with known ...
triple_tactic's user avatar
0 votes
0 answers
57 views

Is "work" a natively physical or natively mathematical concept?

I recently watched a wonderful video explaining the Cauchy and Residue theorems, and how a complex integral's components relate to work done by and flux from the Polya vector field of the function ...
HydroPage's user avatar
  • 157
0 votes
1 answer
75 views

Integral transformation that I don't understand.

I am confused about an integral transformation used in a certain algorithm. The purpose of the algorithm was to obtain distance when accelerating/decelerating without the need to explicitly know how ...
Nathan Weasley's user avatar
2 votes
1 answer
46 views

Decomposition of function into products

Given a single variable function $f(x)$, is there a way of decomposing it into the product of a family of function. Something similar to, $$f(x) = \prod_n p^{a_n}_n(x)$$ I am trying to find the ...
PRITIPRIYA DASBEHERA's user avatar
1 vote
1 answer
62 views

$\ddot x$ vs. $\dot x^2$

I'm working on a physics assignment and am having some trouble. I need to integrate $r\dot\theta^2$ with respect to $t$. However, my trouble lies in the definition of the upper-dot format. Given: $$ \...
Chaserix's user avatar
3 votes
1 answer
71 views

How to evaluate this definite integral in terms of Bessel functions.

In the context of Green's functions for the Free Klein-Gordon field, the following integral occurs: $$\int_m^{\infty}{\rho e^{-\rho r}\over\sqrt{\rho^2-m^2}}\; d\rho.$$ Here $m$, is a positive ...
Albertus Magnus's user avatar
1 vote
0 answers
62 views

particle in motion under the influence of friction

Let's consider a particle of mass = 1 Kg moving according to the law $$ \ddot x(t) = -V'(x(t))-\frac{2}{3}\dot x(t) = -x(t)^3+x(t)-\frac{2}{3} \dot x(t). $$ (The potential energy is $V(x)=\frac{x^4}{4}...
dattiluca's user avatar
0 votes
0 answers
39 views

Finding the trajectories of fluid particles

I have completed the question up to when it asks me to show that up to leading order, the trajectories of fluid particles for these waves are ellipses. I am slightly confused what I am looking for; ...
idk31909310's user avatar
3 votes
0 answers
36 views

Trajectories and Changing Limits of Integration

Although I came across this issue doing physics, the underlying nature of the problem is purely mathematical. So, Work is defined as $W_p=\int_{\gamma_{p}}\vec F_p\cdot d\vec r_{pa}$ where $\vec F_p$ ...
Sebastian Mostek's user avatar

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