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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What if segments are not infinitely divisible?

I almost got myself mixed up I a philosophical discussion again. Somebody was talking about the Planck time and length which are, according to him, the minimal possible time and distance, and how ...
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Finding the distance from a parabola (ballistic trajectory) to a point (for use in collision detection)

I need to have some form of collision detection / prevention for an object moving along a ballistic trajectory and a second stationary object on the same plane plane. The ballistic trajectory is ...
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How to calculate direction of ball upon collision?

I'm creating a game (Breakout) that involves a paddle and ball. I'm having trouble calculating the direction that I should send the ball after collision with the paddle. Currently, upon collision ...
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Approximate an integral

In a physics textbook, I came across the integral $$I(r_1,r_0)=\int_{r_0}^{r_1}\frac{1}{1-2m/r}\left[1-\frac{r_0^2(1-2m/r)}{r^2(1-2m/r_0)}\right]^{-1/2}dr$$ The author said that the integrand can be ...
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Finding the gravitational potential of a tilted disc?

Referring to this question: http://physics.stackexchange.com/questions/62637/the-potential-and-the-intensity-of-the-gravitational-field-in-the-axis-of-a-circ Suppose the disc was tilted at a 30 ...
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Complex Number Plane Physics Math Problem

Show that if the line through the origin and the point z is rotated 90°about the origin, it becomes the line through the origin and the point iz. Use this idea in the following problem: Let ...
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2answers
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what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
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Solving a differential equation?

I'm trying to analyze the transient state of a RC circuit. My book gives me the following differential equation: $$\frac{d(v(t))}{dt} + av(t) = c$$ for some constants $a$ and $c$. The book thens ...
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A question about the Laws of Thermodynamics [closed]

Many popular and semi-popular books about cosmology have appeared during the last few years in which the ultimate fate of the Universe is conjectured. One such scenario stipulates that space will ...
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1answer
67 views

When are $\Delta x$, $\delta x$, $dx$, and $\text{đ}x$ exactly the same? When are they approximately the same?

As a follow-up to this related question, I'd like to know under what circumstances, if any, $\Delta x$, $\delta x$ and $dx$ all mean the same thing, and under what circumstances they can all be said ...
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Second order differential equation for acceleration

Can you help me understand and solve this question: A bullet is fired vertically upwards with an initial velocity of $u$. Form a second order differential equation for acceleration and by ...
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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 ...
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Circular motion h.w [closed]

Need help with homework in this subject. That's the question: Earth rotates around the sun and makes a whole for 365.25 days. The distance between the center of the earth to the center of the sun 150 ...
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1answer
61 views

What's the proper interpretation of canceling infinitesimals?

In most textbooks of physics I've found this demonstration of work-kinetic energy theorem: $$\begin{align} W &= \int_{x_{1}}^{x_{2}} F(x)\ dx \tag{1}\\ &= \int_{x_{1}}^{x_{2}} m\cdot a\ dx ...
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1answer
68 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 ...
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2answers
89 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), ...
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stroboscope effect

I have a disc with a line drawn on one of his radius that is turning with frequency $f$, and I want to sample the place of the line to find the frequency of the disc. So we know from the ...
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Britney gallivant's paper folding formulas

According to a few youtube videos and Newscientist, formulas exist (based on algebraic/mathematical premises, thereby making this a valid math question) to describe the limits of paper folding. The ...
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Why is chemotaxis considered an emergent behavior?

this is an applied math question. I could have posted this under a biological stackexchange, but the idea of emergent behavior or emergent properties of a system seems more appropriate to an applied ...
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1answer
43 views

Interpretation of Riemann rearrangement theorem [closed]

There's a common thing that happens in mathematics, which is that all theorems are created equal, but some are more equal than others. Here are two examples of what I mean by that. (1) In Euclid, the ...
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2answers
90 views

What are integrating factors, really?

I can follow the rationale for integrating factors well enough, but they still feel like voodoo to me. Every single description of integrating factors I've seen (and I've seen quite a few, including ...
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Integration problem related to physics problem

I want to know how to solve this (acytually this is the flux on any non-adjacent side of a cube due to a charge q on the vertice of the cube, side length: l) $$a=\int_0^l\int_0^l ...
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1answer
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Calculating stiffness and dampening for an oscillation to settle at a given time

The Problem How can I calculate a stiffness (k) and dampening (b) coefficient for an under-damped oscillation such that the system settles by a given time (t)? The Environment Given the ...
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1answer
50 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 ...
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0answers
35 views

Variable density in the equation of motion

At a fixed point in time, consider the equation of motion $$ \nabla \cdot \boldsymbol \sigma(u) + \boldsymbol f = \rho \ddot{\boldsymbol u} \quad \text{in $\Omega \subset \mathbb R^d$} $$ for a ...
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How to maximize speed of rest position approach of nonlinearly damped spring oscillator?

Inspired by comments to answer for this question: Suppose we have a system which is described by the equation $$\ddot x=-x+g(\dot x),$$ with initial conditions $x(0)=1$, $\dot x(0)=0$. If ...
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1answer
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Verify that $\nabla(A\cdot B) = (B\cdot\nabla)A + (A\cdot\nabla)B + B\times(\nabla\times A) + A\times(\nabla\times B)$

I'm trying to verify the following identity $$\nabla(\textbf{A}\cdot\textbf{B}) = (\textbf{B}\cdot\nabla)\textbf{A} + (\textbf{A}\cdot\nabla)\textbf{B} + \textbf{B}\times(\nabla\times\textbf{A}) + ...
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1answer
35 views

How can I prove the tangential acceleration equation?

This is my assignment for this weekend. $$a=a_{TT}+a_{NN} = \frac{d^2 s}{dt^2}\vec{T} + \kappa \frac{ds}{dt} 2\vec{N}$$ Actually, I want to why $a_N=\kappa (ds/dt)$ hold Please help me.
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1answer
21 views

Oscillating Object - Homework [closed]

I am forced to post this question here as physics SE refuses homework questions even if tagged with their (severely misleading) 'homework' tag. See my question at: ...
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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 ...
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1answer
35 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 ...
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1answer
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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.
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1answer
35 views

Proving the moment of inertia formula for right cylinder

I have a question on whether I can do this with an integral: When I tried solving this, I got (1/2)(M^2)(R^2) instead of (1/2)MR^2 Problem: http://i.imgur.com/QDdEEse.jpg *Sorry for lack of TeX. ...
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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 ...
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35 views

Physics Related Watt Question

A 550 kg dragster accelerates from rest to a final speed of 110 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts ...
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Helmholtz decomposition - motivation

Our lecturer presented us the Helmholtz decomposition of smooth vector fields. He added a proof, but he didn't provide any single motivation - e.g. where Helmholtz used the decomposition or for which ...
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1answer
24 views

Fastest direction in circular trajectory [closed]

I have a point P and a vector V. This point is describing a uniform circular trajectory with linear velocity lv and angular velocity av. This trajectory passes through a point P', how do I find out if ...
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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 ...
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Retarded function?

How was the sign of the retarded green function chosen? A friend told me it had something to do with the Fourier Transform, but I didn't really understand him. The same explanation might apply to the ...
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16 views

Line VS Circle Collision

Circle: cx, cy, r Line: x1, y1, x2, y2 What is the equation to see if they collide? (2D) I need an equation with it's final end returning true or false, since this is originally a problem for my ...
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1answer
21 views

Resolve A Circle to Rectangle Collision

In 2D, I have a circle and a rectangle, the circle has properties: density: 0.7, velx: 2, vely: 3, rad: 20, centx: 20, centy: 10 and the rectangle has properties: topx: 200, topy: 300, width: 500, ...
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1answer
30 views

Deriving Barometric formula

Recall idea gas law: $pV= NkT$ where $p$ equals pressure, V volume, N moles of atoms, k boltzmann's constant, T temperature. Also, density: $\rho = m/V = \mu N/N_A V$ where $\mu$ is average mole mass ...
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1answer
47 views

Integrating this physics expression

Recall: $dp= \rho g \ dh$ where $dp$ is the change in pressure, $ \rho$ is the constant of density and $dh$ is the change in height. This is a part of fluid dynamics (buoyancy). I am to integrate ...
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1answer
62 views

How do I solve this integral with hyperbolic functions?

I was studying mechanics when I f ound a problem that lead to an integral that I can't solve. Basically the problem asked to find the period of oscillation function of the energy $E$ of a particle ...
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38 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} ...
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1answer
59 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 ...
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1answer
37 views

How do I compute speed based on acceleration and drag?

I'm interested in simulating the (one-dimensional) speed and position of a car. How can I compute the speed $v(t)$ given initial speed $v_0$, acceleration $a(t)$ (I don't want to assume that it is ...
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21 views

Lagrangian of a pendulum inside af disc

I'm currently struggling with a mechanical problem, where I need to find a relationship between the two angles in a mechanical system. The two equations of motions were derived using the Lagrange ...
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2answers
39 views

If Roger is fired from the cannon with an angle of inclination θ of 60° and that he hits…

If Roger is fired from the cannon with an angle of inclination θ of 60° and that he hits the ground 1/2 mile from the cannon. What, then, was Roger's initial speed?
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Help verifying a the correct partial differentiation of $v_0=R\sqrt{\frac{g}{2h}}$

I have to use partial differentiation to solve the below equation: $v_0=R\sqrt{\frac{g}{2h}}$ Where $g$, $R$, and $h$, are defined as follows: $g=9.80 \frac{m}{s^2}$ $R=155 cm$ $h=116.2 cm$ ...