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

learn more… | top users | synonyms

7
votes
0answers
33 views

How can one tell if a PDE describes wave behaviour?

I have been looking at a lot of different non-linear PDEs which describe waves lately and have come to the realisation that I don't know what it is about these PDEs that make them behave like waves. ...
1
vote
0answers
17 views

Physical Object to Pseudo-Riemannian Manifold

It is well known that Lorentzian mainfold is studied in general relativity. So this raises my curiosity about How about the classical mechanics? Does it correspond to the manifold $\mathbb{R}\times ...
0
votes
1answer
25 views

Concerning the notation $\chi (U)$ in one of the hypothesis for some properties of curl and divergence

I have the following exercise: Let $U \subset \mathbb{R}^3$ be open, $X \in \chi (U)$ and $f \in C^{\infty}(U)$, prove the following: $$curl(\nabla f)=0 \\ div(curl(X))=0 \\ curl(f.X)= ...
-2
votes
2answers
38 views

How to calculate the acceleration if the plane on which the object is sliding makes 40 degree angle with ground? [closed]

An object placed on a ramp slides to the ground. If ramp makes angle of 40 degree with ground and object weighs 25 pounds, find the acceleration of the object.
2
votes
1answer
47 views

Magnetic field by current in an infinite cylinder

Let $V\subset\mathbb{R}^3$ be an infinitely high solid cylinder of radius $R$, with its axis coinciding with the $z$ axis, entirely enclosed by the cylinder's lateral surface. Then, for any constant ...
0
votes
2answers
33 views

Trigonometry word problem (involving wires)

A guy wire $78$ feet long runs from the top of a pole $56$ feet high to the ground and pulls on the pole with a force of $290$ pounds. What is the horizontal Pull on the top of the poll? I am not ...
0
votes
1answer
17 views

centroid of a right triangle

I'm asked to find the $M_x, M_y$ and the centroid of the shape created by the functions $5x/6$ and $x=6$ that has a density of $5$. I find $$M_y \int_0^5 \frac{5}{6} x^2dx = \left. \frac{5}{18} x^3 ...
2
votes
1answer
36 views

Finding when velocity is zero

Given trajectory $s(t) = 2t^3 - 15t^2 + 36t + 2$ find, when velocity $v = 0$. I'm doing this the following way: $$v = \frac{ds}{dt} = 6t^2 - 30t + 36.$$ Then making $v = 0$, i.e. $6t^2 - 30t + 36 = ...
4
votes
1answer
35 views

A projectile is launched with a velocity of 30 m/s at 40° to the ground. To two decimal places, what is its horizontal velocity in m/s?

A projectile is launched with a velocity of $30 \, m/s$ at $40^\circ$ to the ground. To two decimal places, what is its horizontal velocity in $m/s$? A ball is thrown downward from the top of a ...
1
vote
2answers
42 views

What kinds of motion obeys a higher order form of angular motion?

Angular velocity $\vec{\omega}$ can be defined in terms of velocity $\vec{v}$ and position $\vec{s}$ as: $$ \vec{\omega} = \frac{\vec{s} \times \vec{v}}{\left\lvert s\right\rvert^2} $$ Constant ...
0
votes
0answers
29 views

Show a beam is in equilibrium given the stress tensor

Having some trouble with this: https://gyazo.com/0835bdaa8e01cb976765aac94555f6ef I know how to show that at x_2 = -h the surface traction is zero, but I'm not sure how to show it's in equilibrium? ...
1
vote
1answer
86 views

Integrate second order DE once

Given the vorticity equation $$\frac{D \omega}{Dt}=(\omega \cdot \nabla)\textbf{u}+ν\nabla^2ω$$ and $\textbf{u} = (−αr/2,v(r),αz) $ in cylindrical polars where alpha is positive constant. Find ...
0
votes
0answers
32 views

About periodic trajectories of a Hamiltonian system

Consider a Hamiltonian system with Hamiltoniana $H (\mathbf{q}, \mathbf{p})$, where $H$ doesn't depend on time $t$. It is known that in some domain of phase space the trajectory of system are peiodic. ...
0
votes
1answer
15 views

Velocity along curve given velocity in one axis

Let's say that I have some particle travelling along a 2D trajectory mapped out by some infinitely differentiable function $f$ (in this case $f(x) = x^{-1}$). I know the velocity of the particle ...
1
vote
0answers
33 views

(Differential Galois Theory) Where is the proof that the three-body-problem is unsolvable?

I'm looking for a proof, which shows that "the 3-body-problem" in physics is mathematically unsolvable. Does anyone know some URLs that contain a proof in mathematical detail? You know, in ...
-1
votes
0answers
32 views

How to prove the orbit of planet is a circle or ellipse?

I think it is enough by $F=ma$ and $F=\frac{GMmr}{|r|^3}$.But I get stuck in a ODE $$ x'(t)=\frac{-GMx(t)}{(x^2(t)+y^2(t))^{3/2}} $$ How to deal it ? Or how to prove the orbit of planet is a circle ...
0
votes
1answer
8 views

Finding the radius of frustum cone?

I'm trying to understand how can i find the radius from the figure , the solution of the radius is given in the equation but I'm not getting how its derived enter image description here
-5
votes
0answers
44 views

Finding the distance between two moving objects

In this case there is a missile whose initial position is $A(30,40)$ with a velocity of $[50,30]$ and an asteroid whose initial position is $B(400,250)$ with a velocity of $[-20,-30]$. The position of ...
0
votes
2answers
60 views

Circuit Analysis problem (find the problem)

In this question, I know that $\text{C},\text{R},\text{T},\text{A}\in\mathbb{R}^+$ I've this circuit (the bottom of the resitor is connected to earth ($0$)): When I use Laplace transform I can find ...
2
votes
2answers
40 views

Second order non linear differential equation: Central force question

The problem is as below: I have derived that the particle satisfies the motion equation $$ \frac{d^2u}{d \theta ^2 } + u = \frac{F(1/u)}{mh^2u^2} $$ by Newton's Law, $u= 1/r$ and $h = r^2 \frac{d ...
2
votes
1answer
28 views

Unique ground state of Schrödinger Operators

I'm reading a book and there is an argument that the ground state of a Schrödinger operator is unique. The problem is I think the argument is complete non-sense! These are lecture notes by Witten, I ...
1
vote
2answers
18 views

If the height of an upwardly thrown ball can be approximated by $h(t)=h_0+v_0t-\frac{g}{2}t^2$, what is $\frac{h(t_2)-h(t_1)}{t_2-t_1}$ conceptually?

I know that it describes the secant through $(t_1,h(t_1))$ and $(t_2,h(t_2))$, but I wouldn't know how to interpret it in "real life" terms. I also know that if $t_1$ tends towards $t_2$, I get the ...
-1
votes
1answer
79 views

Employing Newton's Laws with differential equations [closed]

Going through some problem sheets from previous semesters and can't find a full solution for this question so was wondering what the answers might be. A particle of mass $m$ moves on the $x$ axis ...
3
votes
0answers
27 views

Dissipation term in wave equation

If we're given a string with mass density $\rho$ in units $\frac{M}{L^3}$ with constant cross-section $A$, tension $T$ in units $\frac{F}{L^2}$, and whose length is $L$; and then we assume that the ...
2
votes
1answer
42 views

Ellipsoid moment of inertia matrix

Some background info: torque $\tau$ is defined as $$\tau = I*d\omega$$ Where $I$ is the moment of inertia matrix and $d\omega$ is an object's rotational acceleration. As I understand it, the inertia ...
0
votes
1answer
28 views

Calculate position with increasing acceleration.

So if calculating the change in an object's position (with a constant acceleration) is done with this equation: $o = vt + (\frac12)a t^2$ $o$ is offset from original position $v$ is starting ...
0
votes
1answer
58 views

Parabolic slide

Given a friction-less slide $y=x^2$, place a particle on the slide at $(1,1)$. The particle is acted upon by constant gravity $g= 9.8$ units/s/s. At what time does it reach bottom? The ...
0
votes
0answers
14 views

Modeling population density with PDE

If we know that the population density $u(x,t)$ in some lake varies as a function of $x>0$ and time $t$, where $x$ increases downwards with depth, and that the population diffuses with constant $D$ ...
2
votes
1answer
27 views

Vector Force Application

I have this question for Math StackExchange Site. Suppose you would like to cros a $132 ft$ -wide river in a motor boat. Assume that the motorboat can travel at $7.0mph$ relative to the water and ...
1
vote
0answers
21 views

Writing PDE in the form of convervation law

What does one need to know in order to write $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+\frac{\partial^3 u}{\partial x^3}=0$ in the form of a conservation law, which contains the ...
3
votes
0answers
44 views

Why don't more celestial bodies exhibit higher-order rotations?

It is well known that the Earth spins on its axis. It is also well known that the Earth's axis also precesses, i.e. spins around a secondary axis, much more slowly. Less well known is that we have ...
2
votes
1answer
21 views

Computate the commutator $[p^n,x]=-ihnp^{n-1}$

Computate the commutator of $[p^n,x]=-ihnp^{n-1}$. With $p=-ih \frac{\delta}{\delta x}$ the impulse operator. $h$ stands for $\frac{h}{2\pi}$. Answer: I do it with induction over $n$. For $n=1$ ...
0
votes
2answers
33 views

Two trains and a fly using the series

I'm having some difficulties dealing with this problem: A train starts travelling from A towards B. It's velocity is v. Simultaneously train starts travelling at the same velocity from B to A. The ...
2
votes
1answer
43 views

Pendulum loss/gain of time per day given : $\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$ and max displacement $5^{\angle}$

Here is what i am given: The oscillations of a pendulum are described by the equation: $$\ddot{\phi}+\frac{g}{l}\sin{\phi}=0$$ where $\phi$ is the angle between the pendulum and the vertical axis, ...
10
votes
0answers
79 views

A version of Ampère's law

The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law uses the fact that, if $\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3$, $\boldsymbol{J}\in ...
0
votes
1answer
23 views

What direction would a hinge's reaction force point?

In my homework question there is a ladder with the bottom touching the smooth floor and the other end is attached to a hinge. I need to draw a force diagram and use that to find the normal. There is ...
2
votes
1answer
38 views

Vortex flow - Surface Integral

Consider the vortex flow of a fluid of density $\rho$ where the fluid rotates with an angular velocity $\omega$ about the $z$-axis. Determine where a unit square $S$ on the $yz$-plane should be placed ...
1
vote
0answers
22 views

How would I find the velocity of an object after it doesn't fully enter the gravitational pull of a planet and is kind sling shot out of its gravity? [migrated]

Obviously that question doesn't have a lot of jargon having to do with math and physics. I am not a physicist, I'm not a mathematician, I'm trying to make a game and simulate some physics found in ...
2
votes
1answer
13 views

Dipole-Coupling Tensor: Electrostatic Dipole Moments

I've been struggling with this problem today. Here's an image of the question I'm attempting to answer. I'm relatively new to tensor algebra (I've been studying it for about a week or two), and I've ...
0
votes
2answers
14 views

Calculating quantities with regards to a pendulum

The set up is a pendulum of length 2m with a mass on the end at 0.5kg. The mass is released at a small initial angle of 6 degrees moving into harmonic motion. I need to calculate the angular ...
0
votes
1answer
25 views

two dimensional heat equation

Please I really need some help for this exercise, I can't solve it for any ways... I need to prove the maximum principle for the two dimensional heat equation with zero boundary data. Really I need ...
0
votes
0answers
13 views

Error propagation in complex formula

I'm currently trying to use error propagation formulae to calculate an estimate for the error in the following molecular dynamics formula: $C_v^* = \frac{3}{2}\bigg[1-\frac{2}{3NT^{*2}}\big\langle ...
1
vote
1answer
17 views

calculate the speed of a ball, with a laser

I'm doing a project where I have to calculate the speed of a ball, passing a certain point. I want to do this with a laser, by taking the time the laser is broken in comparison of the ball it's size. ...
1
vote
0answers
28 views

Approaching a Trajectory Problem

I am trying to design a railgun simulation. The idea is that the user can supply a starting point and velocity vector for a launcher and for a target, and the launcher will find the angle to launch ...
1
vote
0answers
31 views

Heat problem with an internal source of heat for which the maximum principle doesn't hold.

Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it... $$u_{t}=u_{tt}+2(t+1)+x(1-x) , ...
2
votes
0answers
39 views

$\frac{\omega}{2\pi}\int_0^{\frac{2\pi}{\omega}}\frac{\sin^2\theta \cos^2\omega t}{(1+\beta\cos\theta \sin\omega t)^5} dt$

I'm going to write out the whole problem as it is given to me (bad grammar and all) even though some of the info may be irrelevant to finding a solution. A charge $e$ moving along a straight line ...
1
vote
0answers
45 views

Uniform current in cylinder and straight wire causing same magnetic field?

The tridimensional version of the Biot-Savart law says that the magnetic field generated at the point $\boldsymbol{r}\in\mathbb{R}^3$ by a tridimensional distribution of current defined by the current ...
1
vote
1answer
25 views

finding curvature radius

given a projectory equation of the form $ y=y(x) $find the curvature radius as a function of $x.$ a projectory equation , hence $ x=x(t)$, input that in y and we get $y=y(x(t))$, which is what one ...
1
vote
1answer
42 views

Instantaneously at Rest. What does it mean?

What is instantaneously at rest? Does it mean that velocity and acceleration must be both 0? So for question, $v(t) = 3 - t/2$, $t>4$, why is $t=6$ instantaneously at rest?