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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1answer
25 views

Statics question: Calculate thrust force [on hold]

First and foremost can someone explain what is being asked here please?
0
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0answers
24 views

Why use class multiplication in Homotopy groups?

This is a related to a physics question Why use class multiplication to describe topological entangling and merging?. In physics, the homotopy theory is used to describing topological defects in order ...
1
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2answers
44 views

Physics: Help me understand this vector problem?

So I'm doing Physics homework - and I already have a rather crappy understanding of vectors, this problem just frustrates me because I have literally 0 idea of what to do with the information it gives ...
2
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3answers
39 views

Projection operator is Hermitian

Use Dirac notation (the properties of kets, bras and inner products) directly to establish that the projection operator $\mathbb{\hat P}_+$ is Hermitian. Use the fact that $\mathbb{\hat ...
0
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0answers
23 views

Intercept planet following an elliptical path (i.e. interplanetary space travel)

So, just as in this question (Intercept path to object following an elliptical path) I have a simple game where I want spaceships to intercept planets, which follow elliptical paths (in my case ...
1
vote
1answer
24 views

Find the speed required for a boat to “catch” a key dropped from a bridge.

So I'm doing a simple Physics homework problem, and I'm honestly unsure if I'm using the proper formulas for each step. The problem is as follows: A key falls from a bridge that is 47 m above the ...
1
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2answers
34 views

Significance and physical meaning of diagonalization of linear maps and bilinear forms, eigenvalues and eigenvectors

In linear algebra, I have studied the diagonalization of a linear map and of a bilinear form; and also the concepts of eigenvalues and eigenvectors. However, the importance of diagonalizing a linear ...
0
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0answers
9 views

Express Kirchoff's first law using power flow.

If we just know the power flow in and out of a junction node, can we say that $\sum\limits_{p: e\in p, i\in e^-} f_p = \sum\limits_{q:e\in p, i\in e^+} f_q, \forall i$, where $f_p$ is the power flow ...
6
votes
1answer
580 views

Damped Harmonic Oscillator and Response Function

This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a driven damped harmonic oscillator, show that the full ...
0
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0answers
11 views

Proving that the derivative of the LRL vector $=0$ [closed]

How to prove that the derivative of the Laplace–Runge–Lenz vector $=0$? $$A=\dot{x}\times(x\times\dot{x})-\dfrac{k}{\mu}\cdot\dfrac{x}{||x||}$$ $$\dot{A}=0$$
4
votes
1answer
115 views

Finding $\mathbf{10}\otimes \mathbf{8}\otimes \mathbf{8}\otimes \mathbf{8}$ in $SU(3)$

I know that in $SU(3)$ $$\mathbf{8}\otimes \mathbf{8} = \mathbf{27}+\mathbf{10}+\mathbf{\bar{10}}+\mathbf{8}+\mathbf{8}+\mathbf{1}. $$ How can one use this to compute $$\mathbf{10}\otimes ...
0
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0answers
8 views

Convert position and velocity vector to TLE for propagation

I have a set of position and velocity vector for a satellite at time t0. I want to propagate position and velocity of the satellite at time t (t>t0) I converted these vectors to Keplerian Elements ...
1
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0answers
25 views

What is the root structure of the Diffeomorphism Group?

Being a physicist, I think it'd be cool to have Coxeter plane projections of the root systems of the symmetry groups associated with the fundamental forces hanging on my walls (example for E8: ...
0
votes
1answer
30 views

Calculate how long a ball will be in the air after being thrown

So I'm doing some online homework, and have done this specific problem 3 different times and gotten the same answer, but the answer I get seems to be wrong? The problem is as follows: (a) With ...
2
votes
1answer
66 views

Differentiating position with respect to 'modified time'

I've been reading a book on orbit determination, and I've hit a block with the calculus. Why do this and is the resulting value even acceleration? This differentiation is very odd to me. He defines ...
0
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0answers
25 views

Stiffnes tensor, Hooke's law

Let's have a deformed body of an isotropic homogenous material. How is it possible that we can write the free energy in the form $$F=F_0+\frac12\lambda\left(\sum_i ...
0
votes
1answer
23 views

Effective Acceleration for Non-Constant Acceleration Motion

This question uses the same symbols as "Effective Acceleration" is Distance-Averaged Acceleration?. One of the kinematics formulas for constant acceleration is: $\Delta x=v_0*\Delta ...
0
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1answer
25 views

Second order differential equation, physics.

I need your input on this exercise I'm doing: "A 2-kg mass is suspended from a string. The displacement of the spring-mass equilibrium from the spring equilibrium is measured to be 50 cm. If the mass ...
1
vote
1answer
46 views

“Effective Acceleration” is Distance-Averaged Acceleration?

My question involves simple math, but to be precise on what I'm asking, I need to write a lengthy description. Let us define the following symbols: $t$: time $x(t)$: distance as a function of time ...
26
votes
8answers
3k views

Very *mathematical* general physics book

I am searching for a book to study physics. So far, I've been suggested Resnick, Halliday, Krane, Physics, but it doesn't seem to be very suited for a math major. Can you suggest some more ...
2
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0answers
96 views

Classical perturbation theory + KAM theory

In classical canonical perturbation theory of many degrees of freedom we encounter the problem of small divisors when attempting to find a solution for the generating function of the canonical ...
0
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2answers
50 views

What are the degrees of freedom of $F=ma$ and $F =mdv/dt$? [closed]

I read in http://en.wikipedia.org/wiki/Degrees_of_freedom, the definition of "degree of freedom" for equations. However, I am consfused about what is the degree of freedom of the two known physical ...
0
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0answers
13 views

Probability - Wind speed calculation

I've been asked to find the probability of wind speed exceeding 15 m/s in a certain area. The question states that a bridge must be shut down if the wind exceeds that value and so my challenge is to ...
15
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4answers
2k views

Why does dust gather in corners?

I've noticed when sweeping the floor that dust gathers particularly in the corners. I assume there is a fluid mechanics reason for this. Does anyone know what it is? Edit: No, really, this is a ...
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0answers
13 views

Issues Calculating Average Acceleration?

So I'm doing a Physics problem here and I'm down to my last answer and I honestly can't figure out where I'm going wrong. The problem is as follows: From t = 0 to t = 4.22 min, a man stands ...
0
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1answer
467 views

Acceleration and Tangential Velocity Vector? <Completely Lost>

Find the resultant acceleration of a particle moving on a circle of radius 0.70 m, if its angular speed is 37 rpm and its tangential acceleration is 2.9 m/s2. Express the angle with respect to the ...
-1
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1answer
27 views

How can I take the derivative of $Q=C \cdot \Delta T$

How can I take the derivative of $$Q=C \cdot \Delta T$$ with respect to time $t$? note: $C$ is heat capacity and $T$ is temperature
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2answers
549 views

Describe a sine wave of known frequency with only two points

This is my first post on math.stackexchange (sorry if meta people remove the Hello (sometimes we do that over on stackoverflow ;P)! I have a system wherein I know that the output is a sine wave, with ...
0
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1answer
13 views

Shifting Velocity and Position functions

I'm given a function $A(t)$ that defines the acceleration of an object w.r.t. time $t$ and am tasked with finding the position function and velocity function for that object. Finding the functions ...
2
votes
1answer
7k views

Finding time with given distance and acceleration. Help Needed

A plane accelerates from rest at a constant rate of $5.00 \, \frac{m}{s^2}$ along a runway that is $1800\;m$ long. Assume that the plane reaches the required takeoff velocity at the end of the runway. ...
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0answers
14 views

Computing the angular momentum in spherical coordinates [migrated]

How to compute the angular momentum of a particle in spherical coordinates? It's given by: $$x_1=r\cdot\cos(\phi)\cdot\sin(\theta)$$ $$x_2=r\cdot\sin(\phi)\cdot\sin(\theta)$$ ...
0
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0answers
12 views

Trouble converting $m^3$/hr to kg/sec

So I'm doing a physics problem on conversions, and having a bit of trouble with the intermediate steps (since I keep getting the wrong answers. The problem is as follows: Suppose that it takes 18.2 ...
0
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0answers
10 views

Lift force formula

Hello! I'm creating a (simple) flight simulation game, and to simulate the aircraft physics up and down movemet as realistically as I can, I'm going to use the Lift force formula. I found the formula ...
1
vote
1answer
39 views

Characteristic of a ring: intuitive explanation

I know the following definition of characteristic of a ring: it is the smallest positive $n$ such that $$\underbrace{a+\cdots+a}_{n \text{ summands}} = 0$$ for every element a of the ring, if $n$ ...
4
votes
2answers
109 views

Why $F(\mathbf q,\dot{\mathbf q},t)$ and not $F(\mathbf q,t)$?

In beginner classical mechanics, which I've just started learning, a particle with coordinates $\mathbf q\in\mathbb R^n$ has its equation of motion specified by $F(\mathbf q,\dot{\mathbf ...
2
votes
1answer
37 views

Find Distance Function from Acceleration Function

The (non-constant) acceleration as a function of time, $a(t)$, is defined and known over $[t_0, t_2]$. It is also known that $a(t)$ is integrable. Also, $a(t)=\frac{dv(t)}{dt}$ and ...
1
vote
1answer
27 views

Relationship between proper orthochronous Lorentz group $SO^+(1,3)$ and $SU(2)\times SU(2)$, or their Lie algebras

I have seen sources claim that $SO^+(1,3) \cong SU(2) \times SU(2)$, but have seen others claim that only their Lie algebras are isomorphic. Is it true that $SO^+(1,3) \cong SU(2) \times SU(2)$? If ...
1
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0answers
28 views

Verify solution to $\frac{i R}{L}+i'=\frac{U_m \sin (\text{$\omega $t})}{L}$

Show that this is a solution $$i(t)\text{:=}\frac{U_m \sin (t \omega -\varphi )}{Z}$$ to $$i'+\frac{i R}{L}=\frac{U_m \sin (t \varphi )}{L}$$ given: $$\varphi =\tan ...
3
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0answers
99 views

“The All-Purpose Calculus Problem” [closed]

Taken from "The Futility Closet" which, in turn, took it from Math Horizons, Spring 1994. The illustration and text are here: ...
5
votes
5answers
238 views

What really are units? And why is it valid to ignore them (once you have dimensional homogeneity), as is done in class?

All my life the approach has been as follows: In math class I learn the rules and almost always deal with purely numerical problems. In physics class I apply the things learned in math class but ...
0
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0answers
9 views

Another box sliding up a ramp question

This is the problem: A woman exerts a horizontal force of 9 pounds on a box as she pushes it up a ramp that is 6 feet long and inclined at an angle of 35 degrees above the horizontal. ...
1
vote
2answers
370 views

Calculating the linear output force a threaded rod and nut would produce based on the input torque

I would like to calculate the amount of linear thrust a threaded rod combined with a rotationally static nut would be able to produce based on the rotary force applied to the rod. The information ...
4
votes
0answers
50 views

Tricky question (physics) [migrated]

I know this may not be the place for this question, by stackexchange physics has banned homework questions :( A piece of hair taken from a goat has a radius of $3.1\times 10^{-5}\text{ m}$. What is ...
6
votes
2answers
588 views

Why can't a perpetual motion polyhedron exist?

I've been thinking about polyhedrons, when placed on a table on a certain face, will tip over and keep tipping over infinitely. I'm trying to prove mathematically that such a polyhedron doesn't exist. ...
3
votes
3answers
159 views

General Solution for the Gravity Between Two 3D Triangles

I would like to find the general solution for the gravity between two (flat) triangles in 3D, including the location $(x,y,z)$ where this force should be applied (in order to later account for ...
3
votes
2answers
308 views

What physical meaning do the dimension of Wigner d-matrices have?

Wigner's D-matrices is defined as $D_{m'm}^j(\phi,\theta,\psi)=\langle jm'|R(\phi,\theta,\psi)|jm\rangle$; it produces a square matrix (indices $m$ and $m'$) of dimension $2j+1$. It is also ...
1
vote
1answer
36 views

Problem with average velocity.

A particle moving in a straight line having acceleration which varies with velocity as $a=-kv^n (n\ne1,2)$. Here k is a constant. For what value of $n$ the average velocity of the particle averaged ...
0
votes
0answers
20 views

Find center of mass and moment applied on beam structure. [migrated]

I have a simple mathematical problem to solve but it is giving me a slightly difficult time to figure out. The problem: I have a beam structure with same cross section. It consists of three beam. ...
0
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1answer
22 views

Railway track and Cyclist crossing, Motion Problem.

A railway track runs parallel to a road until a turn brings the road to railway crossing. A cyclist rides along the road everyday at a constant speed 20 km/hr. He normally meets a train that ...
4
votes
1answer
87 views

A doubt about Differential Geometry Books.

I intend to read "Physics for Mathematicians" by Spivak, and he says that vols. 01 and 02 of "A Comprehensive Introduction to Differential Geometry" are necessary to understand the book. Are those ...