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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27 views

ODE particular solution (physics)

I have to do this exercise: ($Z(t)=I(t)$, it's printed wrong). I have a doubt about the first item. To find all resonance when $R=1$, I found the particular solution $I_{p}(t)=A\sin(\omega ...
0
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0answers
38 views

Partitions applications in physics

Is there any direct application of all developments related to partitions? I am specially interested in physics but cryptography or other mostly theoretical areas would also be a good answer. By ...
5
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2answers
77 views

Solution of differential equation with Dirac Delta

Is it possible to solve a differential equation of the following form? $\partial_x^2y + \delta(x) \partial_x y = 0$ where $\delta(x)$ is the dirac delta function. I need the solution for periodic ...
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1answer
41 views

How to properly generalize a definite integral?

I know, I know. On the can, this problem seems simple. Just take $\int_a^bf(x)\mathrm{d}x$ and write is as $\int f(x)\mathrm{d}x$. However, when I tried to do that on an Engineering Dynamics ...
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3answers
37 views

Rate of change question (planes, kites and the such)

Q: A kite $100 \ m$ above the ground moves horizontally at a speed of $8 \ m/s$. At what rate is the angle between the string and the horizontal, i.e. e the ground, decreasing when $200 \ m$ of string ...
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1answer
42 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
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1answer
22 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
2
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1answer
59 views

How we apply representation theory to physics.

I want to have a concrete idea of what people do with representation theory in physics. Here is what I think: Corresponding to a specific "physics", there is particularly a Lie group (called G) of ...
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0answers
6 views

Inter-neighbor resistance on triangular prism

Given a triangular prism of infinite length along the X direction. A graph is formed with the set of nodes all the points on an edge of the prism with integer values of X, and the with each node ...
2
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3answers
62 views

Representation theory in physics

0 down vote favorite I'm sorry if this is somewhat a dumb question. First: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements ...
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1answer
30 views

Related Rates Questions Calculus [closed]

A particle is moving along the curve $y=2\sqrt{3x+5}$. As the particle passes through the point $(2,9)$, its $x$-coordinate increases at a rate of $4$ units per second. Find the rate of change of the ...
0
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1answer
28 views

How far will my car roll given a function representing the slope of the landscape I'm driving on?

So I was driving in my car thinking to myself "I wonder how far I would go (before starting to roll backwards) if I just took my foot off the brakes" I tried to figure it out myself but could not. SO ...
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1answer
51 views

Why do these acceleration computations contradict each other?

A rocket follows the path $(y-40)^2=160x$ after traveling vertically to the height of 40 feet (making for a very convenient continuity. The problem asks "If the component velocity in the vertical ...
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1answer
20 views

Calculating the force on each of two directions needed to move object to destination

Given the following: How would you calculate the forces needed on the v and u directions to move point ...
2
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2answers
46 views

Differentiation of function

There is a passage in a physics textbook I don't quite follow. Since my question is mathematical, I've decided to post it here. The book says: Let $V$ be the volume of a molecule and assume $V = ...
1
vote
1answer
18 views

Evolution curves on dynamic system

The matrix of a linear dynamic system is: [0, 3] [3, 0] FACT: If A is the evolution curve that passes on point (1,1) in phase space and B the evolution curve that passes on point (1,-1) we can ...
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0answers
51 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
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3answers
109 views

Is speed a function of position?

Let $x$ be a smooth function from $[0,\infty)$ to $\mathbb{R}^n$ satisfying the following differential equation $x''(t) = f(x(t))$, where $f$ is a smooth function from $\mathbb{R}^n$ to itself. Then ...
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2answers
43 views

Magnetic Field Created By Infinite Current Sheet [closed]

So this question is fairly basic, but I haven't quite understood it for a while now. If there is an infinite sheet that has current passing through it and you want to calculate the magnetic field on ...
0
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1answer
25 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 ...
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2answers
32 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.
3
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0answers
92 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
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1answer
22 views

Differential problem in Gausses law

From the Gauss law we know, $\nabla \cdot \vec{E} = \rho / \epsilon_0 $. We have given that, $\vec{E}= kr^3 \hat {r}$ Now I have problem to get the identified part. Can you please elaborate ...
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0answers
21 views

good primer or intro on quenched stochastic processes

I was hoping that someone could recommend a good intro to "quenched" stochastic processes. I am using quenching in the sense of condensed matter physics where systems can present quenched disorder.
0
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1answer
22 views

Limiting a energy term

A famous Einstein's mass energy equivalence equation is $E= \frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$ I need to prove from the above equation is that E = pc. I know that, i will have to limit $m ...
0
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2answers
33 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 ...
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0answers
10 views

Effect of Oscillatory Amplitude.

Hi Guys I did a simulation on a model am currently working on and I discovered that the amplitude of oscillation of solutions to the model is itself oscillatory. I have not see this kind of behaviour ...
0
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2answers
47 views

Finding the average of the absolute value of a function?

I know that to find the absolute value of a function, $$\frac{1}{b-a}\int^b_af(x)\mathrm{d}x$$. This is actually kind of intuitive. The problem is I don't know how to to find the average of the ...
0
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2answers
38 views

Calculate Displacement when velocity is a function of displacement

Particle is moving on a straight line and where velocity varies with its displacement as $v=\sqrt{4+4s}$. Find displacement at t = 2 s if s=0 at t=0. I am not able to figure out how to approach this. ...
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1answer
24 views

How can I read logarithmic scale?

I've got this histograms: How can I read that logarithmic scale? For example, on the histogram 1 there is approximately $10^{-3}$ value at y-axis at 2 value at x-axis. Does it meant that there is a ...
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4answers
73 views

Euclidean Geometry in Physics

I've started tutoring my 13 year old niece in math. She learning geometry this year (it's a year-round school). Obviously, it'll just be basic Euclidean geometry -- though I might try to get to a ...
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1answer
58 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
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1answer
104 views

Please explain the logic behind $d(xy) = y(dx) + x(dy)$

I've seen $d(xy) = y(dx) + x(dy)$, but I don't understand the principle behind it and memorizing it is lame. Can anyone explain what is going on here? For example from physics, $$F = {{dP} \over ...
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2answers
101 views

List of Advanced Math Text Books with answers

Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of ...
6
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2answers
188 views

Seasonal changes in hours of daylight

I will post my own answer to this question unless someone else posts the same answer first, but I am curious to know what other points of view might lead to different ways of answering it. ...
6
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0answers
115 views

How to solve a time-dependent Schrodinger equation in periodic Dirac delta potential

I'm trying to solve a 1D time-dependent Schrodinger equation: $$ i\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} \frac{\partial^2}{\partial x^2}+V(x)+F(t)*x\right]\psi(x,t) $$ where $V(x)$ ...
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1answer
52 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),\\ ...
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0answers
36 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 ...
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3answers
43 views

Solving 2nd-order ODE for SHO

In physics for a Simple Harmonic Oscillator, we have the differential equation $$ {\frac {d^2x}{dt^2}} + \frac kmx = 0 $$ from the balance of forces, which has a solution $$ x(t) = {x_o}\cos(\omega ...
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0answers
72 views

Are there any legitimate examples of applications of set theory to Physics?

Sets are of course ubiquitous, so in this sense set theory is applicable to physics. But I'm thinking more like techniques like forcing, or constructs like cardinals or ordinals. Intuitively it ...
0
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2answers
25 views

How do you scale the change of a period over time?

I am writing a game, and I have a period (a repeating cycle) which is mapped to the scrolling of a background. I want to change this period, so that the scrolling is faster or slower--- but if I just ...
0
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1answer
31 views

Decaying velocity model

I am reading a paper that goes: Here tau accounts for timing and sensor inaccuracies (inherent of the operating system available on mobile phones) by providing a decaying velocity model, ...
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3answers
84 views

Moments at which moving points on a circle coincide

Points A $(0,1)$ and B $(1,0)$ start moving along the circumference of a unit circle with center $(0,0)$ in the same, positive (that is, counterclockwise) direction. Every minute, points A and B ...
2
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1answer
35 views

finding the mass and number of atoms

A small cube of iron is observed under a microscope. The edge of the cube is $4.00 \times 10^{-6}$ cm long. The atomic mass of iron is 55.9 u, and its density is 7.86 $g/cm^{3}$. a) Find the mass ...
0
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1answer
76 views

I can't seem to find this derivative any help would be great.

A rocket of mass m = 1000 kg is traveling in a straight line for a short time. The distance in meters covered by the rocket during this time is described by the function $r(t)=t^3 −3t^2 +6t$ where ...
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1answer
82 views

Does pure math have anything to say about the Lorentz transformation?

The Lorentz factor, $${1 \over {\sqrt {1 - {{{v^2}} \over {{c^2}}}} }}$$ appears intuitively correct from a mathematical viewpoint. According to special relativity, the ratio of the velocity of a body ...
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2answers
84 views

how to calculate vehicle speed using mathematics and Image processing?

i am doing my project in image processing.using segmentation i have detected the moving part(i.e the car) in the video successfully. But now i want to calculate speed of vehicle. in the above ...
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2answers
140 views

Is there a deeper meaning when a number is squared? [closed]

In my opinion, math is about more than just memorizing equations, it's about numbers that are built in a way that represents our understanding of something. So I ask this, what does it mean ...
0
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1answer
16 views

How to find time of man running? (motion formulas)

So for this question there is a man running through a section of grass 1.14375m long at a speed of 3m/s. How do i find his time do i assume the initial velocity is 0? Because that is the only way it ...
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1answer
33 views

Transpose of a differential operator

Let $H$ be a diagonalizable matrix (not necessarily Hermitian). Then, it induces a biorthogonal left and right vectors, such that $$ ...