0
votes
0answers
13 views

How the Jacobian is connected to the movement of particle from one domain to another? [on hold]

I am dealing with the proof of Reynold-Transport Theorem. There the Jacobian is used for the changing position of particles from one domain to another. Can anyone help me to understand what does ...
0
votes
1answer
26 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
62 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
33 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 ...
12
votes
5answers
748 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
172 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
16 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
31 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
28 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
32 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
53 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
60 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
60 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
40 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
57 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
109 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
38 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
60 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
38 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 ...
2
votes
0answers
77 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
votes
1answer
59 views

Force between two parallel wires?

Having two current carrying (currents $I'$ and $I$) wires of length $a$ parallel to the $z$-axis, one with end points $(0,0,0)$ and $(0,0,a)$ and one from $(a,0,0)$ to $(a,0,a)$, I'm looking for the ...
0
votes
4answers
75 views

Multiple choice question on rates of change (or so I thought)

If I were to find the resistance of the component (see image below), I would either find the equation of the curve and use differentiation or I'd draw a tangent at $V_2$ and then find the reciprocal ...
0
votes
1answer
32 views

Angular momentum, rotating rigid bodies, simple example…

Revising, this is what I'm stuck on: inertia tensors, rotating rigid bodies about axis other than its axis of symmety,... I think it'd help a lot to see a worked example and I can't find anything on ...
0
votes
0answers
15 views

Separation of the centre of mass coordinates for an N-electron atom

Can anyone tell me how to derive [A8.5] and [A8.6] in Appendice 8 of "Bransden: Physics of solid state matter", in this screenshot: http://i.imgur.com/zSCkVnI.jpg ? It should be easy, but damn me I ...
1
vote
0answers
26 views

Angular momentum, rotating cylinders,…

Revising, this is what I'm stuck on: inertia tensors, rotating rigid bodies about axis other than its axis of symmety,... I think it'd help a lot to see a worked example and I can't find anything on ...
1
vote
0answers
25 views

plane wave move out

I have a plane wave that is recorded by a set of receivers with x spacing between them (see the sketch). in the sketch (plane wave in black slant line, receivers are the little circles in black and ...
0
votes
1answer
60 views

Fourier-Laplace Transform of Heaviside Step function multiplied to Sine

In a Advanced Solid State lecture I encountered the following assertion- Fourier Transform of $\Theta(t)\sin(\omega_0 t)$ is ...
1
vote
1answer
62 views

Uniform Circular Motion with Banked Road and Car

In Uniform Circular Motion, if a car is rounding a curve at a certain speed, and the angle of the road allows the car to drive around at that speed, that speed is called the "design speed." If the ...
0
votes
0answers
23 views

Is it possible to simulate fluid dynamics in a time-based and deterministic manner?

The Problem Domain I have a number of network-connected PCs. I want to be able to simulate and replicate the same simple fluid dynamics simulation (Eg Navier-Stokes), in real-time, between them. That ...
0
votes
0answers
45 views

Invalid use of the analytic continuation of the Riemann zeta function?

Watching this video on You Tube I got the impression that some sciences (in this case physics) use the analytic continuation of the Riemann zeta function without justification. Maybe this is just my ...
1
vote
2answers
43 views

Calculate velocity after certain displacement

Given is a function $a(t)$ for the acceleration. Starting from an initial velocity $v_0$ I want to calculate the velocity $v_1$ after a certain displacement $s$. Is this calculation possible since ...
-2
votes
2answers
100 views

Studying maths for physicists [closed]

I am looking forward to be a theoretical physicist ,to unify general relativity and quantum mechanics ( to make the theory of everything ) How should I study maths? Should I study proofs of ...
-1
votes
2answers
95 views

Sketching phase portraits [closed]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
2
votes
0answers
49 views

Clarification on some notation and “assumptions” in page 143-144 of the book “Quantum Fields and Strings: A Course for Mathematicians, Volume 1”

I was trying to read the chapter $1$ (at page $143$) of this book Quantum Fields and Strings: A Course for Mathematicians, Volume 1 that is supposed to be an introduction to modern quantum field ...
1
vote
1answer
79 views

How can the tension force be computed to test if a shape is moving or not?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
4
votes
2answers
114 views

A problem about symplectic manifolds in Arnold's book

There is a problem in Arnold's Mathematical Methods of Classical Mechanics which says that: Show that the map $A: \mathbb{R}^{2n} \rightarrow \mathbb{R}^{2n}$ sending $(p, q) \rightarrow (P(p,q), ...
3
votes
1answer
78 views

How to compute force on joints of a 3D structure of balls connected by rods?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
4
votes
0answers
36 views

C. Neumann passage in Latin from *Annali di Matematica Pura ed Applicata*

Neumann, Carl. “Theoria nova phaenomenis electricis applicanda.” Annali di Matematica Pura ed Applicata 2, no. 1 (August 1868): 120–128. doi:10.1007/BF02419606. p. 121: Nova introducitur ...
0
votes
1answer
36 views

Explanation on equations please [closed]

I've got seemingly two different equations for velocity in orbit: $$v_1 = \sqrt{ \frac{2GM}{R}} $$ and $$v = \sqrt{ \frac{Gm_e}{R}}$$ What is the difference between these two? I'm quite sure that ...
0
votes
1answer
19 views

When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
0
votes
0answers
32 views

Shooting a grenade - angle throwing

In my 3D simulation/game I need to shoot a grenade from a grenade launcher. The movement of the grenade is already setup by someone else. all I need is to give him the pitch angle of the grenade ...
2
votes
0answers
29 views

Solution to the “cubic” Helmholtz equation

What is known about the solutions of the differential equation in three-dimensions $$ \nabla^2 \phi = -\kappa^2 (\phi + (1/3!)\phi^3) $$ Without the cubic term, this gives a linear operator ...
0
votes
0answers
41 views

Finding angular momentum about the center of mass?

If we have a couple of particles of an equal, unknown mass: $r_{+} = (c + e^{-Bt} \cos({\theta}))\textbf{x} + (d + e^{-Bt} \sin({\theta}))\textbf{y}$ $r_{-} = (c - e^{-Bt} \cos({\theta}))\textbf{x} ...
2
votes
1answer
63 views

Solve without convergance?

Two days ago I recalled a problem I was given a long time ago. The problem is: Four ants are placed on the vertices of a square with side 1. The ants start moving, each directed towards its left ...
0
votes
1answer
19 views

How to work out 3 dimensional vector angles

I've come across this question and cant for the life of me think how to work it out. I understand working out the angle between two vectors e.g. given, vector a(2i+3j-k) and vector b(8i-6j+2k) but am ...
4
votes
5answers
563 views

What physics book for aspiring theoretical physicist / pure mathematician [closed]

I am a high school student. I want to learn physics on my own, but I am puzzled : Should I read a book which talks about all branches of physics? If yes, recommend a book. Should I read a book which ...
0
votes
0answers
24 views

a group of order 32

Consider the creation and annihilation operators $\left\{a_{1},a_{2},b_{1},b_{2}\right\}$: $$[a_{i},a_{j}]_{+}=0,[b_{i},b_{j}]_{+}=0, a_{i},b_{j}]_{+}=\delta^{j}_{i}$$ with ...
0
votes
0answers
29 views

Calculating where a snowball lands if it doesn't hit anything while falling?

In my calc based physics class we were given the following question, which I've had a lot of trouble with: A snowball rolls off a barn roof that slopes downward at an angle of $40^∘$. The edge of the ...
0
votes
0answers
29 views

Don't understand how this answer is arrived at; dynamic power

According to my notes the fomula for dynmaic energy is $\frac{1}{2}capacitive load \times voltage^2$ and formula for dynamic power is $\frac{1}{2}capaxitive load \times voltage^2 \times switching ...