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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Physics Velocity Correction

So, been up all night working on getting the velocity/angle of arrow simulations perfect. Running into an issue with the physics engine I'm using is ever so slightly off (probably a rounding issue) ...
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0answers
26 views

Averaging speeds

I read the answer to this question: http://stackoverflow.com/questions/34794664/how-should-i-calculate-the-average-speed-by-road-segment-for-multiple-segments/34795821#34795821 Can anyone please ...
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1answer
22 views

Does the momentum of a particle depend on its position [on hold]

By definition: $\displaystyle \dot{x}=\frac{p}{m}$, where $p$ is the momentum of the particle $m$ is the mass, and $\dot{x}$ the velocity. As the velocity depends on the position of the particle(?) ...
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2answers
39 views

Is velocity a function of displacemnt?

The velocity $\displaystyle\vec{v}$ of a particle $=\frac{d\vec{x}}{dt}$. So surely this means that $\vec{v}$ is dependent on the position of the particle?
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0answers
37 views

Acceleration of an air bubble under the sea

An air bubble arises from the bottom of the sea. Find its acceleration if the resistance force is proportional to $\rho$*A*$v$ where $\rho$ is density of water, A is cross section area and $v$ is ...
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1answer
20 views

Examples of physical motivation for integrals over scalar field?

I'm looking for good examples of physical motivation for integrals over scalar field. Here is an example I've found (source): A rescue team follows a path in a danger area where for each position ...
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4answers
67 views

How does computing the determinant of a matrix with unit vectors give you the Cross Product?

Say you had $(a_x,a_y,a_z)\times(b_x,b_y,b_z)$, you would set up a matrix like the following: And the resulting would be your Cross Product or the coordinates of an orthogonal vector. My question ...
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1answer
13 views

Cartesian State Vectors → Keplerian Orbit Elements

So, I've been working my way through the following as I'm messing about with programming some helper functions for orbital mechanics: ...
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1answer
33 views

More equations than unknowns for maxwell equations?

I had one curiosity regarding maxwell equations in 3-D From the curl equations, you get 6 unknowns, with 6 equations. The divergence equations add 2 additional equations. When these are combined, we ...
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1answer
11 views

Momentum change in an inelastic collision

Hello fellow stackexchangers, this is my first post, so sorry if this is too vague or violates guidelines. I am studying Physics and this problem came up, I will type it verbatim A small object ...
2
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0answers
13 views

Gauss-Green cubature in 2d

Hello friends of maths, I've given an arbitrary polygonal cross section (in cartesian coordinates $y$ and $z$). On this cross section, there acts an arbitrary stress-field $\sigma = f(y,z)$ as ...
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0answers
10 views

PDE Von Neumann Problem- Physical Interpretation

The Von Neumann Problem is as such: $\Delta u = f(x,y,z)$ in $\ D$ $\frac {\partial u} {\partial n} = 0$ on bdy $\ D$. Using this you can prove that for there to be a solution to this Von Neumann ...
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1answer
46 views

Do we have $\frac{1}{a} - \frac{1}{b} = b - a$?

I am attempting to prove that $$\frac{1}{E'} - \frac{1}{E} = \frac{1}{m_e c^2} \cdot (1-\cos\theta)$$ can be derived from $$E + m_ec^2 - E' = c^2(p^2 - 2pp'\cos\theta + p'^2) + m_e^2c^4 $$ where ...
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2answers
20 views

Uniformly Accelerated Motion [closed]

Two balls are dropped from different heights. One is dropped 2.85s before the other, but both strikes the ground at thr same time. 8.25s after the first ball was dropped. From what heights where the ...
0
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0answers
17 views

Davenport's Q-method (Finding an orientation matching a set of point samples)

I have an initial set of 3D positions that form a shape. After letting them move independently, my goal is to find the best rotation of the original configuration to try to match the current state. ...
1
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1answer
41 views

How do I use the integral of work to solve the hemisphere pump problem?

I am in Calculus 2 and ran across this problem. The tank (hemisphere) is full of water. Using the fact that the weight of water is 62.5lb/ft3, find the work (in ft-lbs) required to pump the ...
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2answers
39 views

How do I use the integral of work to solve the circular pool problem?

I am in Calculus 2 and ran across this problem. I'm struggling with this subject in general, so I suspect I may be missing something fairly fundamental. A circular swimming pool has a diameter of 14 ...
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0answers
17 views

Runge-Kutta 4 in polar coordinates

How is the Runge-Kutta method implemented on this differential equation: $$ \frac{d^2 \theta}{dt} = -\frac{g}{l} \theta $$ (pendulum motion) which is in polar coordinates? Let: $c = \frac{g}{l}$ ...
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2answers
38 views

Help with Differential equation solution requried

Hi guys I am doing some differential equations and I got this one: I have no idea how he went from (38) to (39). When I solve it by integrating factor, the equation I have is: ...
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1answer
25 views

Velocity Verlet method: How to calculate acceleration

The velocity Verlet method algorithm is as follows: Calculate: $$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t)\, \Delta t+\tfrac12 \,\vec{a}(t)\,\Delta t^2$$ Derive: $\vec{a}(t + \Delta t)$ from ...
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0answers
20 views

Calculating the sun position fails

could you help me find the mistake(s) in my calculation of the sun position today on hawaii at 16:00? I'm following this Wikipedia article. Number of days since 2000/01/01 (2016/01/29): $$n ...
14
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1answer
289 views

Mathematical meaning of certain integrals in physics

While studying on texts of physics I notice that differentiation under the integral sign is usually introduced without any comment on the conditions permitting to do so. In that case, I take care of ...
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0answers
44 views

Understanding derivative notation in those equations

I am given the following set of equations from a physics course, which is about longitudinal waves in rods. My questions are: On the second line you have $ (\frac{\partial \Delta}{\partial x})dx ...
2
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1answer
29 views

Understanding projectile motion formula with air resistance

$\frac{dx}{dt} = v_x$ $\frac{dy}{dt} = v_y$ $\frac{dv_x}{dt} = -b|v|v_x$ $\frac{dv_y}{dt} = -g -b|v|v_y$ where $v = \sqrt{v^2_x+v^2_y}$ and $b$ is a drag constant Why is it that the magnitude of ...
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0answers
18 views

Simple Harmonic Motion; Tension in Elastic rope

I'm struggling to model this question out correctly. A glider and its pilot have total mass $230$ kg. The glider lands on a horizontal airstrip and when its speed is $16$ m/s it hooks on to the ...
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2answers
43 views

Problem about curves. A particle is running along circumference $x^2+y^2=25$

I'm considering a problem about curves. A particle is running along circumference $$x^2+y^2=25$$ with a costant modulus speed compliting a turn in 2 second. I need to determinate the acceleration in ...
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4answers
53 views

Proving $s = ut + \frac{1}{2} at^2 $

I have been asked to prove on a graph that $s = ut + \dfrac{1}{2} at^2 $ I know that the area of the rectangle is $ut$ but the area under the triangle is $\frac{1}{2}\times t \times (v-u)$ So ...
6
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2answers
110 views

Dirac's delta in 3 dimensions: proof of $\nabla^2(\|\boldsymbol{x}-\boldsymbol{x}_0\|^{-1})=-4\pi\delta(\boldsymbol{x}-\boldsymbol{x}_0)$

If $T_f$ is a distribution, i.e. a linear functional, continuous according to the convergence defined here, defined on the space $K$ of the functions of class $C^\infty$ that are null outside a ...
0
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1answer
16 views

velocity with height of time for an arbitrary projectile being launched from a cliff

I have a question about an arbitrary projectile being launched and an arbitrary polynomial describing the height(time) = h(t). The question goes onto ask about the velocity at different points in ...
3
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1answer
59 views

Momentum is quantised in compact spaces?

Background One of the first examples given when studying quantum mechanics is the particle on a cylinder, or particle on a ring. One finds that because of the periodic boundary conditions, ...
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1answer
55 views

How does angular acceleration change with revolutions?

So, for a section of my EPQ (A-Level, Extended Project Qualification), I am trying to analyse a hypothetical circular accelerator using the angular motion equations for constant angular acceleration. ...
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0answers
41 views

What's so special about involute curves??

An involute curve (specifically, an involute of a circle) is very commonly used to define the shape of the teeth on a gear. Apparently this idea goes back to Euler. Why is this? What special ...
2
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1answer
36 views

what is the relation between the Physics Density and the Topological Density

A relation between both is that both deal with how accumulate is something (the notion of density per se), however, I was wondering if there is any "math" relation between both? Thanks
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0answers
12 views

Reference request: 2D conformal field theory and the honeycomb lattice

Would anyone know what is meant by "conformally invariant" functions defined on the plaquettes of the honeycomb lattice (ie the function is defined on the vertices of the dual tringular lattice)? ...
0
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1answer
13 views

How to calculate angle between two objects in orbit

So I have 2 objects in orbit around the same body, and I have all the orbital elements associated with each body. How do I calculate the angle between them both or figure out when they are a certain ...
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0answers
42 views

What's the name of this problem? Interesting minimisation of a length.

There is a problem which has to do with minimising the length of a (possibly disjoint) barrier in a region of space (often a 2D circle) such that no straight line can pass through the particular ...
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2answers
47 views

Noob doubt about signs in equations

I wanted to solve some simple free fall with friction models so I wrote (with $x$ axis orientated down for convenience) $$m\ddot x=mg -k\dot x$$ which I turned in $$m\dot v=mg -kv$$ with $m,g,k$ ...
2
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1answer
35 views

Show, for a sphere, $\langle r^2\rangle = \frac{3}{5}r_o ^2$

The following equation is used as an inference but not explained in my solid state physics book (Economou, "The Physics of Solids"). I figure it's a math/geometry problem so I ask here. Can anyone ...
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1answer
33 views

Maths And Technology: calculating angles of mirrors for a laser.

HELP// maths and technology(light) hello! So, I have a class project in which we have to secure a piece of art in a 'museum'. In this project we have to use a laser, 2 mirrors and a sensor (basic ...
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1answer
18 views

Can I replot a model with an extra axis while saying the exact same thing?

I asked a poorly received question on physics stack exchange, about the universe. Today I left the comment: can we imagine the universe "expanding into nothingness" if we're clear that ...
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0answers
20 views

Density matrix respect to Hilbert space

If there a two dimensional Hilbert sapce $H$ with the basis, $\{ e_1, e_2 \}$ and state $\psi = \frac{e_1 - e_2}{\sqrt{2}}$. How could we express it as a density matrix ?
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1answer
20 views

Rewrite a Lagrange function to Euler-Lagrange equation in polar coordinate

If we have a Lagrange function in the form $L(p, q) = \frac{p^2}{2} + q^2$, how could it be re-written as a form of Euler-Lagrange equation in polar coordinates ?
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0answers
20 views

Two mass spring system [migrated]

The equations of motion of the spring mass system with, m = 1 $ \ddot{y_1} = -k_1y_1 + k_1(y_2-y_1)$ $ \ddot{y_2} = -k(y_2-y_1) - ky_2$ My question is with the second term in the first equation. ...
0
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1answer
12 views

Ski simulation - Velocity vector components

So I am creating a physics ski simulation as a project on my University and the task that I've been struggling with for a couple of hours is: How fast is a Skier moving towards a still obstacle at ...
0
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1answer
30 views

Average Velocity over a time interval

A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation $x(t)= αt^2− βt^3$, where$ α = 1.45 m/s^2$ and $β = 0.055 m/s^3$ ...
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2answers
180 views

Finding the Centroid of a segment

I am having some confusion about the following. As I had never done much physics, this is the first time I have came across the topic. I am asked to find the centroid of the disk segment $x^{2}+y^{2} ...
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0answers
28 views

Conversion of polar equations when you change the position of the origin

I'm working on a physics problem that is described as follows: "I am standing on the ground beside a perfectly flat horizontal turntable, rotating with constant angular velocity w. I lean over and ...
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0answers
34 views

Controlling a flying vehicle with multiple thrusters

I'm working on a problem involving a vehicle with $n$ rocket engines, as seen here: The task is, given the desired force $\vec F$ and torque $\vec \tau$, calculate the optimal thrust for each ...
0
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2answers
91 views

phys questions referring vectors

Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces A⃗ , B⃗ , and C⃗ shown in the figure below Find the magnitude of a fourth force on the stone that ...
4
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0answers
39 views

Calculate the resistance between 2 adjacent nodes on a shape using graph theory

In shapes like regular octahedron or dodecahedron, how can Graph Theory be used to calculate the resistance between two adjacent vertices? All edges are assumed to have unit resistance. Is there ...