0
votes
1answer
25 views

physical meaning of heat equation

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
0
votes
0answers
42 views

Proof of Kepler's first law

Has Kepler ever provided proof of his first law? I've found some articles on the web which use some of the Newton's formulas to prove it but Kepler died before Newton was born. So how did Kepler ...
0
votes
0answers
21 views

Momentum Representation vs Position Representation

I have a question involving the representation of operators in momentum representation and position representation. The question is a little long, so I'll do my best to explain it. We are given an ...
0
votes
1answer
32 views

Calculating the electric field of a disk

I'm having trouble regarding how to calculate the electric field of a disk. Here's the scheme: The exercise states that the disk is uniformely charged. This is what I did: Density charge : ...
5
votes
1answer
97 views

Guide to mathematical physics?

I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ...
1
vote
1answer
67 views

how to solve the system of differential equations for this particle?

I'm trying to solve this problem A particle of mass m moves under the action of gravity on the inner surface of a paraboloid of revolution $x^2+y^2=az$ which assumed frictionless. Obtain the ...
0
votes
0answers
18 views

Explain why we describe the flow of fluid passing through volume with this equation

I am new to this Q&A site. Recently I came across this expression while watching a video http://www.youtube.com/watch?v=GveJWPr9UOk/ about the mass of fluid flowing in through a cube. You can find ...
2
votes
1answer
51 views

Electromagnetism and thermodynamics(Statistical mechanics) books for the mathematician?

I found some very good classical and quantum mechanics,special relativity,gauge theory books for the mathematicians,but I couldn't find anything on electromagnetism or thermodynamics,are they of not ...
0
votes
1answer
15 views

Regularity of the surface of a crystal

If I want to model the surface of any random crystal, is it safe to assume that it is the graph of a Lipschitz function. Is there a precise result from physicists? How wrong would it be if I assume ...
2
votes
2answers
102 views

Set theory and physics [closed]

I would like to know if there are some physical concepts (preferably accessible ones like force, torque, ...) that can be significantly better understood when looked at in the light of concepts taken ...
1
vote
1answer
24 views

Simultaneous Suvat help [closed]

I learnt this in college but can't for the life of me remember how to do it. I've searched stack exchange and the internet for answers but it isn't clicking. It doesn't help my teacher has decided to ...
0
votes
2answers
41 views

How far down will the ball travel and what is the magnitude of the ball's initial vector?

Confused a little with $V_x$ and $V_y$ components and how to find the displacement of X. A football is kicked with an initial velocity of $V_x = 30 \text{ ft/sec}$, and $V_y=80 \text{ ft/sec}$ 1) ...
1
vote
1answer
52 views

Integral of voltage, $\int_{-a}^a \frac{dy}{\sqrt{x^2 + y^2}}$

This is (probably) a very easy integral to solve, but for some reason the answer just isn't coming to me (or at least the one my professor got isn't). He gave us a formula for voltage along the x-axis ...
4
votes
1answer
65 views

Electrostatic Potential Energy integral in spherical coordinates

I'm having trouble with evaluating an integral that arises from attempting to find the total energy of an electrostatic system consisting of two point charges, which involves an integral over all ...
0
votes
1answer
36 views

Show that requiring Electrostatic potential to be a stationary point of Electrostatic potential energy is equivalent to Laplace's equation.

Suppose we want to find the electrostatic potential $\phi$(r) inside of some volume $V$ with known boundary conditions. The physical field configuration should minimize the electrostatic potential ...
1
vote
0answers
43 views

Diagonalization of total angular momentum over creation operators for an isotropic harmonic oscillator?

You have an isotropic three dimensional quantum harmonic oscillator so the Hamiltonian is $$ H=\frac{p^2}{2}+\frac{r^2}2 $$ If you do the creation-annihilation operator-algebra trick and define ...
1
vote
1answer
24 views

Books for Tensor Algebra used in Physics?

I'm taking a dual Math,Physics undergraduate course.I want to study GR and a few parts of relativistic Quantum Mechanics.I've a decent amount of knowledge in linear algebra. Though we have tensor ...
0
votes
0answers
14 views

Heinrich Hertz on Mathematical Equations

What is the quote from Heinrich Hertz on how he could never exhaust the meaning behind a mathematical equation? (It's not mentioned in the Hertz quotations here.)
0
votes
1answer
19 views

one-dimension motion

A rock is thrown vertically up at 80 ft/s. Find it's maximum height, time of flight, and final velocity as it passes the starting point. So for my parameters I have: initial y=0 final y=? ...
1
vote
1answer
30 views

Prove $ \nabla \cdot (f \nabla \psi ) = \nabla f \cdot \nabla \psi + f \nabla ^2 \psi $ in general curvilinear coordinates.

Prove $ \nabla \cdot (f \nabla \psi ) = \nabla f \cdot \nabla \psi + f \nabla ^2 \psi $ in general curvilinear coordinates. I have been attempting to do this using general curvilinear dot products ...
1
vote
1answer
18 views

Find the average acceleration

Find the average acceleration of the tip of the 2.4-cm long hour hand in the interval noon to 6pm. I found the average velocity is -2.2x10^6 but I'm not sure how to go about finding acceleration. If ...
0
votes
1answer
31 views

help setting up a velocity question

Standing on the ground from 3.0 m from a building, you want to throw a package from your 1.5- shoulder level to someone in a window 4.2 m above the ground. At what speed and angle should you throw ...
0
votes
0answers
52 views

Relative motion question

You wish to row straight across a 63-m-wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 0.57 m/s. I know I need to draw a right triangle for the question but ...
1
vote
1answer
35 views

List of well-known submodular function in physics, statistics, math?

Can you please share a list of well-known submodular functions (have the diminishing return property) that you know? In physics, stats, math, etc? I am searching for a submodular function for my ...
1
vote
1answer
189 views

Work on Springs using Hooke's Law

I'm currently stuck on parts c and d of this problem. The problem says Suppose a force of 20 N is required to stretch and hold a spring 0.4 m from its equilibrium position (0). I found k constant to ...
2
votes
0answers
32 views

Liouville's theorem (Hamiltonian) [closed]

can some one give me a link for a rigorous proof for Liouville's theorem (Hamiltonian) thanks
0
votes
2answers
23 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
0
votes
2answers
22 views

Finding vertical displacement

I am being asked to find the distance a shuttle travels upward after a given amount of time. I know that time passed is 79s, the rate of acceleration is 6.244 m/s^2, and the speed at 79s is 493.276 ...
3
votes
1answer
49 views

How to mathematically determine if the magnitude of a cross product is up/down(positive/negative?)?

So, I'm a newbie at complex vector math. I'm working on a 2D physics engine, and my issue is, with angular acceleration from torque, is it supposed to be positive or negative? I understand the right ...
1
vote
2answers
72 views

Water Refraction and the depth of the water.

I'm not sure if this is the right place to ask my question! But I hope I will find some help!. Image distortion occurs by refraction of light at the boundary surface between air and water when a ...
2
votes
1answer
54 views

Why does a heating model work?

I am referring to: $T=T_0 e^{kt}$ where T=temperature,t=time and k=constant. It seems to work, I as just curios to why it works?
0
votes
1answer
53 views

Trigonometry in projectile motion

I initially posted this question on Physics SE but got no responses probably because it's more related to maths than physics. A plane surface makes an angle $\bf X$ with the horizontal. From the ...
3
votes
0answers
63 views

My orbiting body is orbiting about the wrong focus of it's elliptical orbit… why? [closed]

I am coding in c++ and am computing the position of an orbiting body as a function of time. Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it ...
0
votes
0answers
35 views

Subject to in equation

I have the formula below: $$\hat x_2=\arg\min\lVert x\rVert_2\quad\text{subject to}\quad A{x}=y.$$ But I didn't understand what was meant by "subject to" ? does $x$ is replaced by $x_2$? please can ...
13
votes
5answers
815 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
10
votes
2answers
185 views

Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ...
1
vote
0answers
26 views

Basis representation for non-negative, compact support, reasonably smooth spectral function

I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis ...
2
votes
0answers
32 views

Can a quaternionic Kähler manifold be NOT Kähler?

I have an explicit construction of the metric on the quaternionic Kähler manifold $$\mathcal M = \frac{Sp(1, 1)}{Sp(1) \times Sp(1)}.$$ Arranging the four real degrees of freedom into two complex ones ...
0
votes
0answers
30 views

Properties of functional integration

this question comes from theoretical Physics, the issue being the so called Path Integral. The measure of this thing is something written as $[d\phi]=\prod_x d\phi(x)$ And this should be the limit ...
0
votes
0answers
46 views

derivation of an equation involving the Fourier transform of the square modulus of a wave function

A textbook on electron optics states that, ignoring a factor of 2 for convenience, the result $\mathscr{F}(I(\vec{r}))=\mathscr{F}(\phi(\vec{r}))\cdot{}A(\vec{k})\cdot{}\sin[\gamma(\vec{k})]$ can be ...
1
vote
3answers
66 views

integral of the sphere describing lambertian reflectance

A Lambertian surface reflects or emits radiation proportional to the cosine of the angle subtended between the exiting angle and the normal to that surface. The integral of surface of the hemisphere ...
1
vote
1answer
65 views

Formulation VS Interpretation

I'm reading a book on Mathematical Physics and at some point the author says that we must distinguish between a "formulation" and an "interpretation" of a theory, although it's not easy to point what ...
1
vote
0answers
67 views

Resources for learning Relativity

I´m looking for books to the study of Relativity. I know that this is math stack schange and not physics stack schage, but I believe that some of the users here are interesed in physical-mathematical ...
0
votes
1answer
53 views

Centre of Mass and Moment of Inertia of a sphere - spherical cap

I have been given a sphere of radius a, from this sphere a cap of hight h is cut off. 1) What is the centre of mass of the rest of the sphere? 2) What is the moment of inertia regarding the axis of ...
1
vote
2answers
124 views

is it necessary that curl of 2d vector is perpendicular to the plane.

I am just confused, help me guys. The question comes up, because we say that curl is either clockwise or anti-clockwise at a point.
2
votes
0answers
114 views

If physical space had cardinality larger than $\aleph_1$, would we need new math to describe dynamics? [closed]

If physical space had cardinality larger than $\aleph_1$, would we need new math to describe dynamics? For instance, would the dynamics of a sea of virtual particles of cardinality $\aleph_1$ would ...
0
votes
2answers
69 views

Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
1
vote
1answer
60 views

Mathematics/Mechanics Problem

I would like to ask you if anybody could help me with this problem. So far i know that the positions where B and A have to meet are at distances L and L+2r
1
vote
1answer
70 views

Calculating a double pendulum

consider the following situation of a double pendulum. We found the moving equations as $$ \ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\sin(\theta_2-\theta_1),\\ ...
1
vote
0answers
41 views

Why is the space of trajectories for a particle a cotangent bundle?

In Paugams book, Towards the Mathematics of Quantum Field Theory, he writes the following in the introduction: Let us first illustrate this very general notion by the simple example of Newtonian ...