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.
6,001
questions
0
votes
1
answer
23
views
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 ...
- 107
0
votes
1
answer
25
views
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 ...
- 3,555
0
votes
0
answers
41
views
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
$$
B_z = \frac{\mu_0 NI}{2} \left( \frac{\frac{l}{2}...
- 113
-2
votes
1
answer
47
views
Magnitude of Instantaneous Velocity $=$ Instantaneous Speed Rigorous Proof [closed]
In physics, for an infinitesimal time period
$\lvert dr \rvert = ds $
Where $dr$ is displacement and $ds$ is the distance covered.
I understand this idea intuitively but am eager to know a rigorous ...
0
votes
0
answers
22
views
Finding the optimal surface enclosing a given volume
I would like to find, over the set of continuous surfaces that enclose a volume $V$, the one(s) that lead to the maximal value of a certain cost function. I'm working on a physics problem which ...
- 36
0
votes
1
answer
56
views
How to solve this equation analytically
when considering the problem of solving how much mass of fuel does a rocket need in order to leave earth, we come across this equation:
$$
v_{\infty}=-\frac{g}{Q}m_c+u\ln(1+\frac{m_c}{m_f})
$$
Where $...
- 125
-1
votes
1
answer
64
views
I want a formal mathematical definition of the configuration space of a system (mathematically defined examples appreciated)
The Wikipedia article on configuration space offers this "formal definition":
In classical mechanics, the configuration of a system refers to the position of all constituent point particles ...
- 884
1
vote
0
answers
35
views
How to accurately average a function with a nonlinear response?
I am a physics PhD student working in optics and I have a bit of a weird problem that I am trying to sort out and I'm hoping you math folks can help me with.
Without boring you with the experimental ...
5
votes
0
answers
51
views
Optimal length of rope for sliding across a gap
I'm trying to solve a physics problem that I heard ~10 years ago in undergrad that was casually posed to me without a solution in mind; it has been bothering me ever since! Please let me know if this ...
- 252
1
vote
1
answer
52
views
A PDE problem: heat eqaution with variables separation method
I have to solve a PDE problem called "Heat equation":
$
\begin{cases}
u_t = a^2u_{xx}+2xt,0<x<1, t>0 \\ u_x(0,t)=-1, u(1,t)=t \\ u(x,0) = 1-x-\cos(\frac{7\pi}{2}x)
\end{cases}
$
I ...
- 13
1
vote
4
answers
103
views
How does the solution make sense for this ODE about distance and time?
I have an equation: $$ \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 ...
- 77
1
vote
1
answer
62
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 ...
- 323
0
votes
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 ...
- 1
3
votes
1
answer
172
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 ...
- 135
0
votes
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_{...
- 56