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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2
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22 views

Vector/Tensor analysis, Elastic Waves

So I'm fairly confused at the moment. For reference, I'm reading this document, and the current area of interest is Section 7: Characteristic Surfaces for Planar Waves. I'm not gonna give too much ...
0
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1answer
28 views

What are the real and imaginary parts of this complex propagation constant?

I am currently looking at the propagation constant $\gamma\in\mathbb{C}$, which is $$ \gamma = i\omega\sqrt{\mu\epsilon-i\,\frac{\sigma\mu}{\omega}}, $$ where $i^2 = -1$ and all other quantities are ...
1
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2answers
29 views

Physics-projectile motion-finding the angle

An object is fired from a cliff 50m high, at an initial velocity of 100 m/s at an unknown angle. You have to find the angle required to fire the object to a bucket 10m away that is 2m tall. I have ...
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2answers
24 views

Finding the flux of $\iint \vec F\hat n\;ds$

I need to find the flux $\displaystyle\iint \vec F\hat n\;ds$ of the vector feild $\vec F=4x \hat i-2y^2\hat j+z^2 \hat k$ throughe the surface $S=\{(x,y,z):x^2+y^2=4,z=0,z=3\}$ My attempt: (I'm ...
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0answers
19 views

Given a transformation, find the generating function

There's a mapping $(x,y) \mapsto(u,v)$ given by $u= x\cos\theta-y\sin\theta$ $v =x\sin\theta + y\cos\theta$ I'd like to find a generating function $G(x,y)$ for this mapping, which I understand to ...
1
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1answer
62 views

Units of ODE solution don't match

I have to solve the differential equation: $v\,'=g-cv$. Sorry in advance for lack of latex. I will learn it soon, please let me make a question using the common programming notation for my ...
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0answers
49 views

How can I use the Bullet-Physics's ray-cast normal to calculate angles for a object to lay on a surface?

[Give the normal of a surface in XYZ format, how do I calculate rotations (also in XYZ format) needed to set an object parallel to the surface?] I have a collision library that uses the bullet ...
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1answer
12 views

How to divide a vector on a sphere into northern and southern components?

Suppose we have $S^2$ and a vector $\vec{A}$ pointing at a random direction. Let us divide the sphere into $S_N$ for $0 \leq \theta \leq \frac{\pi}{2}$ and $S_S$ for $\frac{\pi}{2} \leq \theta \leq ...
-1
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2answers
38 views

Solving for the resonant frequencies of a mass-spring system

Given 3 masses ($M_1, M_2, M_3$) connected linearly with 2 springs ($K_1,K_2$), let $X_1,X_2,X_3$ be the displacement of the masses relative to their rest positions. Using the Lagrangian I can write ...
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0answers
12 views

Modeling smoke cloud as expanding Gaussian / ellipse

I am making a simplified model of smoke coming from a train's smokestack. You can imagine that if you want an accurate model you have to think in 3D and use computational fluid dynamics and stochastic ...
2
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3answers
56 views

kinetic energy approximation

If a pitcher throws a pitch at a velocity $v_0$, then the kinetic energy is $E_0=\frac 12mv_0^2$. If the pitcher releases the pitch from x feet higher, then we will suppose that he can readjust his ...
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1answer
44 views

How can we explain energy (or intensity) distribution mathematically? [closed]

We have the following scene: We can see that in this scene, there are places which are very bright and there are places which are dark (shadows). I want to know, how can we explain this energy (or ...
1
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1answer
48 views

Triple Integral Using Cylindrical Coordinates

Find the total mass of the solid defined by the inequalities $x^2 + y^2 + z^2 \ge 1, \hspace{.1cm} x \ge 0,\hspace{.1cm} y \ge 0$ with mass density $z^2$. I know I have to use triple integrals to ...
2
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3answers
56 views

potential energy

Let $t_1$ be the time it takes an object to fall $x$ feet. The kinetic energy of a ball of mass m dropped vertically $x$ feet is $E_1=\frac 12mv_1^2$, where $v_1=h'(t_1)$. Find the formula for $E_1$ ...
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0answers
11 views

Question about Spring mass damping system ?? [closed]

I have a spring mass damping system with mass = 6 gram, spring constant = 157000 N/m, damping co efficient = 6.7 N/m, input y(t) = 20 um. is it necessary that doubling mass from 6 to 12 gram would ...
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1answer
43 views

Application of fixed point theory in Physics

Is there any application of fixed point theory in Physics?
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0answers
47 views

Integrate $\int_{-\infty}^{+\infty} \frac{1}{\sqrt{P(x)}}e^{-ax^2 - bx - c}dx$ where $P$ is a polynomial of degree $6$

From a physics problem I'm interested by a closed form of this integral : $$\int_{-\infty}^{+\infty} \frac{1}{\sqrt{P(x)}}e^{-ax^2 - bx - c} dx$$ where $P(x) = \lambda_6 x^6 + ... + \lambda_0$ I ...
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0answers
19 views

How do I find the angular momentum and the energy of a central force?

I've been studying classical mechanics with Symon's book and I'm having trouble when I have to find the energy and angular momentum for a given potencial if the particle moving in a circular orbit, ...
1
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1answer
58 views

Heat equation — Modelling a real-life situation

I have read through a lot of books and lecture notes that cover the heat equation and I am still not sure how I would model the easiest real world situations. For example, take a rod at constant ...
2
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1answer
33 views

Defining a partial derivative with respect to an antisymmetric tensor/matrix

I'm looking at some nonlinear electrodynamics, and have been following a textbook which contains a primer on some of the stuff I'm interested in following up. However, I seem to have fallen at the ...
1
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1answer
30 views

Impact of two bodies problem

A body of mass $M$ moving with a velocity $u$ collides with another of mass $m$ which rests on a table. Both the balls are perfectly elastic and smooth and the the body of $m$ is driven in a ...
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1answer
13 views

Curvature at a point in a vector valued function

I am trying to determine the curvature when $t=2$ of the function $r(t)=<t^3,3t^2,8t>$ So I found $v(t)=<3t^2,6t,8>$ and $a(t)=<6t,6,0>$. So now that I have these two functions, I ...
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2answers
48 views

If you flip a quarter, what are the odds that you will land on that little piece on the edge? [duplicate]

If you were to flip a quarter what is the probability you will get the quarter to land on it's little edge? How would you calculate this? Assuming the probability is not $0$ and is instead a really ...
1
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1answer
25 views

How do I calculate the gravitational force exerted by a thin ring of uniform mass M?

I'm working on a problem and can't seem to get it. Find the gravitational force exerted by a thin uniform ring of mass M and radius a on a particle of mass m lying on a line perpendicular to the ...
0
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1answer
20 views

unit vectors: solving with component method and graphical method

P and Q are vectors in the X , Y plane, have the same magnitude, and are perpendicular to each other. If Q=3.0i+4.0j. What is P?
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1answer
53 views

A problem on collision of two elastic spheres

Two elastic spheres, each of mass $m$ collide directly. Show that the energy lost during the impact is $m(u^2-v^2)/4$, where $u$ and $v$ are their relative velocities before and after impact. ...
2
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1answer
54 views

Stuck on computing distance travelled from velocity and yaw rate.

I am somewhat stymied on what appears to be a simple formula. Here is the problem statement: Assume that a rigid body is traveling with constant velocity $v$, and is rotating with a constant yaw rate ...
0
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1answer
41 views

Methods of Calculating Position

Suppose we have the following code (Euler Method?) to determine Position versus Velocity, Acceleration and Time: ...
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0answers
24 views

Sphere intersecting a triangle

I'm studying "game physics" programming, and in this article, at page 14, I don't understand how is the author right. ... if the sphere does indeed collide with the inside of the triangle then a ...
3
votes
2answers
58 views

Functional Derivative ${\delta q_a(t)}/{\delta q_b(t')}$

$\newcommand{\fdv}[2]{\frac{\delta #1}{\delta #2}}$ $\newcommand{\dv}[2]{\frac{\mathrm{d} #1}{\mathrm{d}#2}}$ $\newcommand{\pdv}[2]{\frac{\partial #1}{\partial #2}}$ I'm from a physics background and ...
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1answer
18 views

How to generate the icosahedral groups $I$ and $I_h$?

The icosahedral groups $I$ with 60 elements and $I_h = I \times Z_2$ are also three dimensional point groups. However, ever unlike other point groups, it seems there is rarely reference to give their ...
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1answer
30 views

Finding constant acceleration required to hit a target where mag(a) = n

I am currently using the equation: $$ \vec p=\frac12\vec at^2+\vec vt+\vec x$$ to find the acceleration I need to move from one point to another. where: $\vec p$ = target position (point 2d) ...
1
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1answer
23 views

Mechanics: Projectiles involving a ball shot out of a cannon, moving in the opposite direction of the shot

A child is playing with a toy cannon on the floor of a long railway carriage. The carriage is moving horizontally in a northerly direction with acceleration $a$. The child points the cannon ...
0
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1answer
41 views

Significance of 'faces' in Stress tensor components?

I am trying to understand what the significance is of the face for which a force is acting on when talking about a stress tensor. Say we consider the components $T_{xx}$ and $T_{zx}$ of the stress ...
4
votes
1answer
65 views

The real equation of a pendulum

In physics I never solve the equation $\ddot\theta = \sin(\theta)$. Instead, we used the approximation $\theta = \sin(\theta)$ for small angles and then it was easy to solve. I didn't do any physics ...
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3answers
63 views

Figure out the component of a value in X and Y coordinates using trigonometry.

Alright. It's been long that I studied trigonometry and did Laws of Motion and Free Body Diagrams, and I was decent good at them, but somehow I am having trouble in understanding the following. Note ...
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0answers
50 views

A problem on Constrained Motion

Q. A particle is moving in a smooth curve under gravity and its velocity varies as the actual distance from the highest point. Prove that the curve is a cycloid. Attempt: The eq. of motion is ...
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0answers
65 views

Why do people prefer cosine to sine when speaking of harmonic oscillation?

In almost all of the physics textbooks I have ever read, the author will write the oscillating function as $$x(t)=\cos\left(\omega t+\phi\right)$$ My question is that, is there any practical or ...
0
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1answer
29 views

solving equation in terms of $w_1$ and $w_2$

I have a a physics problem involves the following equation $$\tan(\alpha) = \frac{(w_1 + w_2)^{1/2}}{w_3}$$ from a certain set of equations that I use I derive the following equation: ...
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2answers
60 views

Practical use for negative $dt.$

I am writing a section of notes for Calculus 1 on related rates. In the section where I discuss differentials, I write that the quantity $dt$ must be nonnegative. I imagined the only reason it would ...
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1answer
65 views

What's wrong with my math in this function to update the position of a planet near a star?

Initially the code seems to work as the planet curves toward the star, but then as it should either get pulled into the star or make an orbit, it just gets pushed away in the opposite direction. What ...
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1answer
33 views

Connecting a mathematical solution to a differential equation with it's physical solution

I have seen this question in a neuroscience course: It is given after the lecture with these and these slides. I have no background in physics. However, I do know how to solve a differential ...
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1answer
10 views

Setting constant as a function of all the variables expect the one we integrate on

I am having trouble fully grasping the concept of setting a constant as a function of other variables: I would like to use a particular example where I could explain my thought process. Hopefully you ...
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1answer
32 views

Following a simplification of expression

I am struggling with this expression: In particular I get stuck with the simplification from the first to the second line. As far as I can see they replace $\text{m$\ell $}=\mu$. Does the new ...
10
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2answers
107 views

what would a planetary orbit look like if gravity had constant magnitude?

Consider a unit-mass particle that is always experiencing a single unit-magnitude force towards the origin. This is a central force, but it is not one of the familiar ones, e.g. gravity whose ...
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1answer
69 views

What is the ratio of the intensities of the two sounds?

1. Suppose that a jet engine at 50 meters has a decibel level of 130, and a normal conversation at 1 meter has a decibel level of 60. What is the ratio of the intensities of the two sounds? we ...
4
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3answers
70 views

How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$

How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$? Is integration the only way? Homogeneous charge distribution ...
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1answer
42 views

How to derive the weak form of the PDE?

I have some difficulties solving the weak form of the PDE: The proof of the preceding statement is elementary. The weak form of the PDE $\nabla \cdot (A(x) \nabla u) + \omega^2 q(x) u = 0$ for all ...
3
votes
1answer
79 views

Counter exchanging limit and integral

Background I came across this answer on Math SE which claimed it made a lot of sense to switch limit and integral. In response I came up with the following counter-examples: $\lim_{w \to 0} ...
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2answers
52 views

Why is the potential function defined differently in physics and calculus?

I am very familiar with the concept of a potential function, and potential energy, from calculus-based physics. For instance, if we have the familiar force field $\mathbf{F} = -mg \,\mathbf{j}$, then ...