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
votes
0answers
212 views

What categorical mathematical structure(s) best describe the space of “localized events” in “relational quantum mechanics”?

In a recent (and to me, very beautiful) paper, entitled "Relational EPR", Smerlak and Rovelli present a way of thinking about EPR which relies upon Rovelli's previously published work on relational ...
6
votes
1answer
807 views

How can angular velocity or angular momentum be a vector?

Rotations in 3 dimensions are not commutative; however they are in the plane. In classical mechanics, are we allowed to say that angular momentum is a vector because particles only rotate along a ...
2
votes
3answers
974 views

Pendulum with moving pivot

I'm making a game which you can see here, if you are on Windows or Linux: http://insertnamehere.org/birdsofprey/ If you click and hold your mouse on a bird, you can see I'm just swinging the bird ...
4
votes
2answers
382 views

How is moduli of curves relevant in physics?

From: http://en.wikipedia.org/wiki/Moduli_space we see that moduli of curves is a very algebro-geometric topic. It is easy to understand its relevance and importance in algebraic geometry. But the ...
13
votes
4answers
3k views

Can this gravitational field differential equation be solved, or does it not show what I intended?

This is the equation I'm having trouble with: $G \frac{M m}{r^2} = m \frac{d^2 r}{dt^2}$ That's the non-vector form of the universal law of gravitation on the left and Newton's second law of motion ...
4
votes
1answer
640 views

Center of mass of an $n$-hemisphere

Related to this question. Note that I'm using the geometer definition of an $n$-sphere of radius $r$, i.e.$ \{ x \in \mathbb{R}^n : \|x\|_2 = r \} $ Suppose I have an $n$-sphere centered at $\bf 0$ ...
3
votes
0answers
117 views

Analysing an optics model in discrete and continuous forms

A discrete one-dimensional model of optical imaging looks like this: $$I(r) = \sum_i e_i P(r - r_i)$$ Here, the $e_i$ are point light sources at locations $r_i$ in the object and $P$ is a point ...
1
vote
1answer
603 views

Using differential equations to graph velocity over time of a falling object subject to wind resistance

Wind resistance -- upwards acceleration, typically varies either linearly or quadratically by the current velocity. There is a constant downward acceleration due to gravity. How can we model the ...
10
votes
2answers
2k views

Finding Moment of Inertia (rotional inertia?) $I$ using integration?

I just came back from my Introduction to Rotational Kinematics class, and one of the important concepts they described was Rotational Inertia, or Moment of Inertia. It's basically the equivalent of ...
90
votes
8answers
6k views

Importance of Representation Theory

Representation theory is a subject I want to like (it can be fun finding the representations of a group), but it's hard for me to see it as a subject that arises naturally or why it is important. I ...
10
votes
2answers
3k views

What is the optimum angle of projection when throwing a stone off a cliff?

You are standing on a cliff at a height $h$ above the sea. You are capable of throwing a stone with velocity $v$ at any angle $a$ between horizontal and vertical. What is the value of $a$ when the ...
85
votes
19answers
4k views

Good Physical Demonstrations of Abstract Mathematics

I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to ...