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.
6,142 questions
1
vote
0
answers
43
views
Asymptotic Taylor-Maccoll Equation as Freestream Mach Number Approaches Infinity
I asked a question a few years ago on Computational Science Stack Exchange. Recently, I was able to implement a solution to this problem, shared the code, and posted it as a follow up.
The solution to ...
- 391
1
vote
0
answers
66
views
How does a half-twist change the energy of a thin vortex ring in an ideal fluid?
Consider a thin vortex ring in an inviscid incompressible fluid ($\mathbb{R}^3$). The ring has circulation $\Gamma$, core radius $a$, and loop radius $R$, with $R \approx a$ (a "fat" ring at ...
- 11
0
votes
1
answer
410
views
Can the function $g(y)=\frac{d}{dy}\int_{y_0}^{y}\frac{dx}{f(x)}$ be simplified without integration?
Let's assume monotonically increasing, continuous, non-linear function $f(x)$ with $f(0)=0$. Can the function
$$g(y)=\frac{d}{dy}\int_{y_0}^{y}\frac{dx}{f(x)}$$
be simplified without knowing the ...
- 59
0
votes
0
answers
60
views
Energy of a torus vortex at $R/r =\sqrt2$ in an incompressible inviscid fluid
I'm looking for the total hydrodynamic energy of a steady vortex torus in an unbounded, incompressible, inviscid 3D fluid, where the ratio of major radius $R$ to minor (tube) radius $r$ is exactly $\...
- 11
0
votes
1
answer
180
views
How to prove that $\sum_j \delta_{ij} \cdot \delta_{jk} = \delta_{ik} $ [duplicate]
My Mathematical Methods in Physics course has just begun, and we have been introduced to functions such as the Kronecker-Delta and Levi-Civita symbols.
We were assigned a problem asking us to prove ...
12
votes
1
answer
727
views
Analytic proof of value of integral arising in electrostatics
The following triple integral arises in electrostatics, when trying to find the electric flux of a uniformly charged hemispherical shell through its flat circular base:
$$
I = \int_{x=0}^1 \int_{\...
- 10.3k
1
vote
0
answers
90
views
Purely mathematical solution to a physics question: finding the period of a particle moving in uniform circular motion. [closed]
This will seem like a primitive and rather uninteresting conclusion, but I was messing around with questions in James Stewart's Multivariable Calculus 5e. Particularly Chapter 14, Problems Plus 1(b):
...
- 39
6
votes
2
answers
264
views
Newtons second law with NSA - why is this logical inference illegal when applying Newtons second law to infinitesimal elements?
I am thinking about some physics applications of nonstandard analysis (NSA). In particular, I am considering what happens to a weak version of Newtons second law as we try to apply the Newtonian ...
- 1,595
0
votes
1
answer
87
views
Why is the jerk equal to the velocity in orbital mechanics?
In Sec. 1.4.2 of BWE, item 3 gives the cross product. The second term should be
$\mathbf{r\times \dddot{r}}$ (which I learned is called the jerk) and then it is equal to $\mathbf{r\times \dot{r}}$. ...
- 125
0
votes
0
answers
48
views
How does the delta-function identity work when defining retarded time in Liénard–Wiechert potentials?
In the derivation of the Lienard-Weichert electric potential, I am up to the point where we have
$$
\Phi(\mathbf{r},t)=\frac{q}{4\pi\epsilon_0}\int\frac{\delta(t'-t_R)dt'}{|\mathbf{r}-\mathbf{w}(t')|},...
- 241
5
votes
2
answers
247
views
Using nonstandard analysis to solve fluid dynamics physics problem
I am currently taking a course in fluid dynamics and was wondering if one might apply non-standard analysis to prove a certain result. I will try to provide all necessary prerequisite knowledge such ...
- 1,595
-1
votes
2
answers
564
views
Why is there little mathematical research in Nuclear Physics? [closed]
Mathematics and Physics have always been very close.
Even though everyone has a different definition of what Mathematical Physics (or even Physical Mathematics, whatever that means) really studies, we ...
- 819
2
votes
0
answers
105
views
"Portals" in $\mathbb{C}$: branch cuts that translate function arguments
First some background and motivation.
I recently came across a YouTube video where the creator tried to calculate the effects of portals on the gravitational field (although electrostatics should work ...
- 109
1
vote
0
answers
67
views
Definition for plane wave equations term
I am working on Exercise 3.4 from a book by Douglas Abraham which is given in the scan below, and a wave equation type problem. I have a result but I believe I am not sure what a term means, namely $\...
- 71
0
votes
0
answers
65
views
Counting sign factors in the Majorana condition without choosing a gamma-matrix representation
I am considering Majorana spinors. My aim is to develop an explanation of spinor theory without using any specific representation of the gamma matrices. I present my setup and the problem below.
...
- 21
