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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8
votes
1answer
731 views

Does apparent retrograde motion of planets begin and end at quadrature?

I've read it several places that the apparent retrograde motion of planets (during which they seem, as viewed from Earth, to move in the opposite sense of their normal "direct" orbital motion against ...
1
vote
3answers
137 views

Help with odd partial derivatives in velocity $\bar v^2 = \dot x ^2+\dot y^2$

I am doing a physics -course Tfy-0.2061. My teacher claims that this is velocity squared, $\bar v^2 = \dot x ^2+\dot y^2$. I cannot understand why it is not $\bar v^2 = (\dot x +\dot y)^2$. If ...
2
votes
3answers
219 views

Calculus and Physics Help!

If a particle's position is given by $x = 4-12t+3t^2$ (where $t$ is in seconds and $x$ is in meters): a) What is the velocity at $t = 1$ s? Ok, so I have an answer: $v = \frac{dx}{dt} = -12 + 6t$ ...
2
votes
2answers
436 views

What is the geometric, physical or other meaning of the tetration?

What is the geometric, physical or other meaning of the tetration or more high hyperoperations? Is it exists in general or it has only math concept?
3
votes
0answers
506 views

Equation of motion for a wobbling disc

While looking at a frisbee the other day, I suddenly had a question. Suppose (in free space) you set a disc-shaped object spinning, and then you impart a sudden force perpendicular to the spinning ...
2
votes
1answer
446 views

Finding the 'inhomogeneous' plane wave solutions of the wave equation via Fourier analysis

When one solves the wave equation $$ ( \partial_t^2 - v^2 \nabla^2) \mathbf{E}(\mathbf{x},t) = 0 $$ in $\mathbb{R}^3 \times \mathbb{R} $ using the Fourier transform method, the general solution is ...
0
votes
1answer
220 views

Function whose graph resembles the shape in this image

What is the function whose graph would resemble the shape found in the image below? I looked this up on Wikipedia, tried making my own, but I can't find an equation the Electromagnetic Spectrum. I ...
2
votes
1answer
187 views

What does it mean mathematically to set some of the integration constants in the general solution to a linear differential equation, equal to zero?

I'm trying to calculate the position of a particle in a quadrapole magnet depending on the entry position $x_0$ and the combined (constant) physical parameters $k$. Given an equation $$x(t) =\frac{(...
0
votes
1answer
1k views

Effects of gravity on diffusion [closed]

I'm just now learning the diffusion model and it seems that we aren't taking into account the acceleration due to gravity of the particles. Is this a shortcoming of the model or irrelevant? I don't ...
1
vote
2answers
179 views

Basic conceptual diffusion problem

Suppose that some particles which are suspended in a liquid medium would be pulled down at the constant velocity V by gravity in the absence of diffusion. Taking into account the diffusion, find the ...
4
votes
1answer
115 views

Is $\Delta^2V$ one of the nature's favourite patterns?

I was reading Sawyer's Prelude to Mathematics, he says that there's one suposed nature's favourite pattern which is: $$\Delta^2V$$ He also says that this pattern is found in a dozen areas: conection ...
6
votes
2answers
95 views

Thermodynamic relation

$$\left(\frac{dU}{dT}\right)_p= \left( \frac{\partial U}{\partial T} \right)_v + \left( \frac{\partial U}{\partial V}\right)_T \left( \frac{\partial V}{\partial T}\right)_p$$ Using maxwell relations ...
0
votes
2answers
302 views

How to find focal length of a convex lens?

I need help finding the focal length of a single convex lens. The radius of curvature is 200mm. left side is air and the glass has a index of 1.5. I search on google but there was only formulas for ...
0
votes
1answer
53 views

The signage of a displacement vector?

Well, on my homework I had these two questions, but got a bit confused about what they are asking, and whether my answer is right or not. What is the sign of the displacement if you are moving ...
0
votes
0answers
59 views

When can I treat vectors as regular variables when differentiating?

Given this Lagrangian where $\dot{\vec r} = \left(\dot x, \dot y, \dot z\right)^T$: $$ L = \frac m2 \left|\dot{\vec r}\right|^2 - q \left( \phi - \left\langle \dot{\vec r}, \vec A \right\rangle \right)...
0
votes
2answers
2k views

Find initial velocity given initial speed and rate of deaccelration?

Okay, So we are going over vectors in class, given Cartesian coordinates and convert them to polar, and vice-versa. So the question is that a skateboard rolls up a ramp shown in the image shown, at a ...
1
vote
1answer
581 views

Parametric curve of intersection - line integral with respect to arc length

This comes from Apostol's Calculus, Vol. II, Section 10.9 #14: A uniform wire has the shape of that portion of the curve of intersecion of the two surfaces $x^2+y^2=z^2$ and $y^2=x$ connecting the ...
1
vote
1answer
276 views

Physical meaning of spline interpolation

I remember that when I took my Numerical Analysis class, the professor said the spline interpolation take its name from a kind of wood sticks used to draw curved lines. Also Wikipedia say that the ...
1
vote
1answer
1k views

Scientific notation ratio conversion?

I wanted to know if I was thinking about this problem right and set it up correctly. It's been a while since I had to do math like this. The radius of the hydrogen atom is $0.529\times10^{−10}m$ and ...
2
votes
4answers
560 views

Trying to find angle at which projectile was fired.

So let's say I have a parabolic function that describes the displacement of some projectile without air resistance. Let's say it's $$y=-4.9x^2+V_0x.$$ I want to know at what angle the projectile ...
2
votes
1answer
99 views

solution for ODE problem

I was trying to simulate a physical system which lead me to this equation. I don't know if it has any solution or not, but I guess you guys can help me find the answer. $$v'(t) = a + s * \frac{v(t)}{...
0
votes
1answer
74 views

Yet another differential equation

Hello, I would appreciate any help solving the following equation: $$\begin{align} y''[t] + \dfrac{d}{m}y'[t] + \dfrac{k}{m}y[t] = G \\ \end{align}$$ subject to: $$t[0] = t0$$ $$t'[0] = 0$$ This is ...
3
votes
2answers
264 views

Help solving differential equation

I want to solve the following differential equation: $y[t]$ : vertical position (height) of the object at time t $y_c$ : height of the ceiling $y_e$ : equilibrium point, the height at which the ...
5
votes
1answer
516 views

Galilean transformations

How do you prove that every galilean transformation of the space $\mathbb R \times \mathbb R^3$ can be written in a unique way as the composition of a rotation, a translation and uniform motion? ...
4
votes
2answers
105 views

What do I need to know to simulate many particles, waves, or fluids?

I've never had a numerical analysis course so I don't know what I need to know. I'm just wondering what kind of books I should get to make me able to simulate these things. I'm wanting to simulate ...
0
votes
2answers
127 views

Questions about $su(2)$. [closed]

Edit: In physics, it seems that people usually study $su(2)$ but not only $sl(2)$? Why people study $su(2)$ but not only $sl(2)$?
7
votes
1answer
6k views

What is a cyclic integral?

Can anyone explain what a cyclic integral is? My professor used it in his Thermodynamics lecture. One of the equations was $$\oint\:dv=0$$ where $v$ is Volume. Isn't the integral of $dv$ equal to $...
0
votes
1answer
351 views

Motion profile, the maximum velocity allowed from stop

I´m trying to calculate what the maximum allowed velocity for a mechanical axis traveling towards a stop. The maximum velocity must be a secure speed so the axis have is able to stop in time. I have: ...
4
votes
1answer
684 views

How come in classical mechanics we can get away with writing $a=v(dv/dx)$, treating $v$ as a function of $x$?

In classical mechanics we often use the relation $a=v(dv/dx)$ to help solve differential equations. I assume when we write $dv/dx$, we really mean $dV/dx$, where $V$ is a function defined so that $V(x(...
6
votes
4answers
600 views

Applications of Operator Algebras to modern physics

I think that recently I've started to lean in my interest more towards operator algebras and away from differential geometry, the latter having many applications to physics. But while taking physics ...
3
votes
2answers
120 views

Why is the landing footprint an ellipse?

Following the Curiosity landing I noticed that the possible landing site (the so-called 'landing footprint') was demarcated by an ellipse. Here is a picture of it: Now obviously such a footprint ...
1
vote
3answers
699 views

Projectile Motion

Hello Stack Exchangers! I'm developing a video game. One feature requires an archer be able to target an enemy and shoot an arrow at it. I've looked around and found plenty of guides on how to do ...
1
vote
1answer
67 views

Question about Lie superalgebra.

What are the generators and relations for the Lie superalgebra $\mathfrak{psu}(2, 2 | 4)$? Thank you very much.
2
votes
2answers
2k views

Wave Equation Neumann Boundary Conditions

I am studying basic PDEs and I would like to ask a thing I can't understand. I would really appreciate a piece of advice. I must compute the solution $u(x,t)$ of a 1-D wave equation with Neumann ...
2
votes
0answers
488 views

Schaum's Outlines for self-study

I wish to learn Physics via self-study. I realize that I have a long way to go as far as Mathematics prerequisites: I will need to begin with Precalculus(I took that course many years ago, so I am ...
5
votes
1answer
3k views

Simple simple Euler Lagrange Equation

Just starting a course on Lagrangian Mechanics and I'm just wondering what about the Euler-Lagrange equation, and more specifically what I'm meant to be trying to do .. One of the questions from my ...
1
vote
1answer
308 views

Specifying plane waves

I'm having trouble understanding how to specify a transverse wave (including it's longitudinal axis and transverse direction) in 3d space. I know this is called a "plane wave", and I know the formula ...
1
vote
1answer
3k views

How do I update position using velocity, acceleration and friction with variable time?

Without friction it is simple, because velocity changes linearly over time, so I can multiply average velocity with $timeDelta$. $$ velocity_{next} = velocity + acceleration * timeDelta $$ $$ ...
0
votes
3answers
141 views

physics related question

i am trying to calculate simple problem from physic,but i am getting somehow wrong answer.problem is that what is a mass of bag which is hold by child with mass $50$KG,if there is force of ...
2
votes
0answers
325 views

Decomposing products of spinor representations into anti-symmetric tensors

There is always a natural $2^{[\frac{d}{2}]}$ dimensional spinorial representation of $SO(d-1,1)$ (..induced from a representation of the related Clifford algebra..) and if $[m]$ denote the space of ...
1
vote
2answers
167 views

Extra dimensions in strings

In string theory there are more than 3+1 dimensions of the space-time, but this is only at very very small "scales", and the concept of dimension used in physics are the one of manifolds because this ...
5
votes
1answer
471 views

Expressing the wave equation solution by separation of variables as a superposition of forward and backward waves.

(From an exercise in Pinchover's Introduction to Partial Differential Equations). $$u(x,t)=\frac{A_0 + B_0 t}{2}+\sum_{n=1}^{\infty} \left(A_n\cos{\frac{c\pi nt}{L}}+ B_n\sin{\frac{c\pi nt}{L}}\right)...
3
votes
2answers
92 views

Approximated solution to differential equation in the form $f(u)u'^2+(u-u_0)^2=k$

I'm trying to solve the following differential equation, that arises from conservation of energy in a physical problem. $R,k$ are constants. $$(1+R^4u^4)u'^2+(u-u_0)^2=k$$ Now, according to my book I ...
1
vote
1answer
66 views

How to define Mach Subsonic by the Mach Supersonic?

I read the book Mechanic of fluids shames and I find this relationship: $$\frac{1+kM_1^2}{1+kM_2^2} =\frac{M_1}{M_2} \left ( \frac{1+\dfrac{(k-1)}{2}M_1^2}{1+\dfrac{(k-1)}{2}M_2^2} \right )^{0.5}$$ ...
19
votes
7answers
3k views

Using mathematics in theoretical physics

I'm a non-mathematician who is self-studying mathematics. Although I'm very interested in mathematics, my main purpose is to apply math in theoretical physics. The problem is that when I read a ...
2
votes
1answer
200 views

Are there introductions to mathematics through physics?

I'm studying mathematics through three books: Calculus: Early Transcendentals, Stewart; Discrete Mathematics, Kevin Ferland; Polynomials, Barbeau. I have also some invitations to mathematics which ...
0
votes
2answers
109 views

Determine the flow and amplitude equation for thermal energy (with Del operator)

It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
6
votes
3answers
960 views

Physical interpretation of the Lie Bracket

I've come accross this physical interpretation for $ [X,Y] $ which I don't understand : Follow $X$ for some time $\epsilon$; Follow $Y$ for $\epsilon$; Follow -X for $\epsilon$; Follow -Y for $\...
4
votes
1answer
624 views

Torque calculation, to achieve clean spin+tumble

Here's a pencil-like robotic spaceship carrying an experiment, it is a solid mass 100m long, 100 inches thick and weighs 1000kg. We're in deep solar space 100au above the sun. Assume we can apply ...
9
votes
1answer
2k views

How does a harmonic oscillator with nonlinear damping behave?

It is well known that for a harmonic oscillator with linear damping, $$\ddot x+c\dot x+x=0$$ with positive $c$, the amplitude of the oscillations decays exponentially when $c<2$. If it is higher ...