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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4
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1answer
113 views

Is $\Delta^2V$ one of the nature's favourite patterns?

I was reading Sawyer's Prelude to Mathematics, he says that there's one suposed nature's favourite pattern which is: $$\Delta^2V$$ He also says that this pattern is found in a dozen areas: conection ...
6
votes
2answers
94 views

Thermodynamic relation

$$\left(\frac{dU}{dT}\right)_p= \left( \frac{\partial U}{\partial T} \right)_v + \left( \frac{\partial U}{\partial V}\right)_T \left( \frac{\partial V}{\partial T}\right)_p$$ Using maxwell relations ...
-1
votes
2answers
285 views

How to find focal length of a convex lens?

I need help finding the focal length of a single convex lens. The radius of curvature is 200mm. left side is air and the glass has a index of 1.5. I search on google but there was only formulas for ...
0
votes
1answer
53 views

The signage of a displacement vector?

Well, on my homework I had these two questions, but got a bit confused about what they are asking, and whether my answer is right or not. What is the sign of the displacement if you are moving ...
0
votes
0answers
58 views

When can I treat vectors as regular variables when differentiating?

Given this Lagrangian where $\dot{\vec r} = \left(\dot x, \dot y, \dot z\right)^T$: $$ L = \frac m2 \left|\dot{\vec r}\right|^2 - q \left( \phi - \left\langle \dot{\vec r}, \vec A \right\rangle ...
0
votes
2answers
2k views

Find initial velocity given initial speed and rate of deaccelration?

Okay, So we are going over vectors in class, given Cartesian coordinates and convert them to polar, and vice-versa. So the question is that a skateboard rolls up a ramp shown in the image shown, at a ...
1
vote
1answer
540 views

Parametric curve of intersection - line integral with respect to arc length

This comes from Apostol's Calculus, Vol. II, Section 10.9 #14: A uniform wire has the shape of that portion of the curve of intersecion of the two surfaces $x^2+y^2=z^2$ and $y^2=x$ connecting the ...
1
vote
1answer
250 views

Physical meaning of spline interpolation

I remember that when I took my Numerical Analysis class, the professor said the spline interpolation take its name from a kind of wood sticks used to draw curved lines. Also Wikipedia say that the ...
1
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1answer
1k views

Scientific notation ratio conversion?

I wanted to know if I was thinking about this problem right and set it up correctly. It's been a while since I had to do math like this. The radius of the hydrogen atom is $0.529\times10^{−10}m$ and ...
2
votes
4answers
537 views

Trying to find angle at which projectile was fired.

So let's say I have a parabolic function that describes the displacement of some projectile without air resistance. Let's say it's $$y=-4.9x^2+V_0x.$$ I want to know at what angle the projectile ...
2
votes
1answer
99 views

solution for ODE problem

I was trying to simulate a physical system which lead me to this equation. I don't know if it has any solution or not, but I guess you guys can help me find the answer. $$v'(t) = a + s * ...
0
votes
1answer
73 views

Yet another differential equation

Hello, I would appreciate any help solving the following equation: $$\begin{align} y''[t] + \dfrac{d}{m}y'[t] + \dfrac{k}{m}y[t] = G \\ \end{align}$$ subject to: $$t[0] = t0$$ $$t'[0] = 0$$ This is ...
3
votes
2answers
261 views

Help solving differential equation

I want to solve the following differential equation: $y[t]$ : vertical position (height) of the object at time t $y_c$ : height of the ceiling $y_e$ : equilibrium point, the height at which the ...
5
votes
1answer
470 views

Galilean transformations

How do you prove that every galilean transformation of the space $\mathbb R \times \mathbb R^3$ can be written in a unique way as the composition of a rotation, a translation and uniform motion? ...
4
votes
2answers
105 views

What do I need to know to simulate many particles, waves, or fluids?

I've never had a numerical analysis course so I don't know what I need to know. I'm just wondering what kind of books I should get to make me able to simulate these things. I'm wanting to simulate ...
-1
votes
2answers
119 views

Questions about $su(2)$. [closed]

Edit: In physics, it seems that people usually study $su(2)$ but not only $sl(2)$? Why people study $su(2)$ but not only $sl(2)$?
6
votes
1answer
5k views

What is a cyclic integral?

Can anyone explain what a cyclic integral is? My professor used it in his Thermodynamics lecture. One of the equations was $$\oint\:dv=0$$ where $v$ is Volume. Isn't the integral of $dv$ equal to ...
0
votes
1answer
323 views

Motion profile, the maximum velocity allowed from stop

I´m trying to calculate what the maximum allowed velocity for a mechanical axis traveling towards a stop. The maximum velocity must be a secure speed so the axis have is able to stop in time. I have: ...
4
votes
1answer
667 views

How come in classical mechanics we can get away with writing $a=v(dv/dx)$, treating $v$ as a function of $x$?

In classical mechanics we often use the relation $a=v(dv/dx)$ to help solve differential equations. I assume when we write $dv/dx$, we really mean $dV/dx$, where $V$ is a function defined so that ...
5
votes
4answers
561 views

Applications of Operator Algebras to modern physics

I think that recently I've started to lean in my interest more towards operator algebras and away from differential geometry, the latter having many applications to physics. But while taking physics ...
3
votes
2answers
113 views

Why is the landing footprint an ellipse?

Following the Curiosity landing I noticed that the possible landing site (the so-called 'landing footprint') was demarcated by an ellipse. Here is a picture of it: Now obviously such a footprint ...
1
vote
3answers
665 views

Projectile Motion

Hello Stack Exchangers! I'm developing a video game. One feature requires an archer be able to target an enemy and shoot an arrow at it. I've looked around and found plenty of guides on how to do ...
1
vote
1answer
65 views

Question about Lie superalgebra.

What are the generators and relations for the Lie superalgebra $\mathfrak{psu}(2, 2 | 4)$? Thank you very much.
2
votes
2answers
2k views

Wave Equation Neumann Boundary Conditions

I am studying basic PDEs and I would like to ask a thing I can't understand. I would really appreciate a piece of advice. I must compute the solution $u(x,t)$ of a 1-D wave equation with Neumann ...
2
votes
0answers
434 views

Schaum's Outlines for self-study

I wish to learn Physics via self-study. I realize that I have a long way to go as far as Mathematics prerequisites: I will need to begin with Precalculus(I took that course many years ago, so I am ...
5
votes
1answer
3k views

Simple simple Euler Lagrange Equation

Just starting a course on Lagrangian Mechanics and I'm just wondering what about the Euler-Lagrange equation, and more specifically what I'm meant to be trying to do .. One of the questions from my ...
1
vote
1answer
295 views

Specifying plane waves

I'm having trouble understanding how to specify a transverse wave (including it's longitudinal axis and transverse direction) in 3d space. I know this is called a "plane wave", and I know the formula ...
1
vote
1answer
2k views

How do I update position using velocity, acceleration and friction with variable time?

Without friction it is simple, because velocity changes linearly over time, so I can multiply average velocity with $timeDelta$. $$ velocity_{next} = velocity + acceleration * timeDelta $$ $$ ...
0
votes
3answers
141 views

physics related question

i am trying to calculate simple problem from physic,but i am getting somehow wrong answer.problem is that what is a mass of bag which is hold by child with mass $50$KG,if there is force of ...
2
votes
0answers
294 views

Decomposing products of spinor representations into anti-symmetric tensors

There is always a natural $2^{[\frac{d}{2}]}$ dimensional spinorial representation of $SO(d-1,1)$ (..induced from a representation of the related Clifford algebra..) and if $[m]$ denote the space of ...
1
vote
2answers
165 views

Extra dimensions in strings

In string theory there are more than 3+1 dimensions of the space-time, but this is only at very very small "scales", and the concept of dimension used in physics are the one of manifolds because this ...
5
votes
1answer
433 views

Expressing the wave equation solution by separation of variables as a superposition of forward and backward waves.

(From an exercise in Pinchover's Introduction to Partial Differential Equations). $$u(x,t)=\frac{A_0 + B_0 t}{2}+\sum_{n=1}^{\infty} \left(A_n\cos{\frac{c\pi nt}{L}}+ B_n\sin{\frac{c\pi ...
3
votes
2answers
91 views

Approximated solution to differential equation in the form $f(u)u'^2+(u-u_0)^2=k$

I'm trying to solve the following differential equation, that arises from conservation of energy in a physical problem. $R,k$ are constants. $$(1+R^4u^4)u'^2+(u-u_0)^2=k$$ Now, according to my book I ...
1
vote
1answer
65 views

How to define Mach Subsonic by the Mach Supersonic?

I read the book Mechanic of fluids shames and I find this relationship: $$\frac{1+kM_1^2}{1+kM_2^2} =\frac{M_1}{M_2} \left ( \frac{1+\dfrac{(k-1)}{2}M_1^2}{1+\dfrac{(k-1)}{2}M_2^2} \right )^{0.5}$$ ...
18
votes
7answers
3k views

Using mathematics in theoretical physics

I'm a non-mathematician who is self-studying mathematics. Although I'm very interested in mathematics, my main purpose is to apply math in theoretical physics. The problem is that when I read a ...
2
votes
1answer
198 views

Are there introductions to mathematics through physics?

I'm studying mathematics through three books: Calculus: Early Transcendentals, Stewart; Discrete Mathematics, Kevin Ferland; Polynomials, Barbeau. I have also some invitations to mathematics which ...
0
votes
2answers
109 views

Determine the flow and amplitude equation for thermal energy (with Del operator)

It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
6
votes
3answers
922 views

Physical interpretation of the Lie Bracket

I've come accross this physical interpretation for $ [X,Y] $ which I don't understand : Follow $X$ for some time $\epsilon$; Follow $Y$ for $\epsilon$; Follow -X for $\epsilon$; Follow -Y for ...
4
votes
1answer
564 views

Torque calculation, to achieve clean spin+tumble

Here's a pencil-like robotic spaceship carrying an experiment, it is a solid mass 100m long, 100 inches thick and weighs 1000kg. We're in deep solar space 100au above the sun. Assume we can apply ...
9
votes
1answer
2k views

How does a harmonic oscillator with nonlinear damping behave?

It is well known that for a harmonic oscillator with linear damping, $$\ddot x+c\dot x+x=0$$ with positive $c$, the amplitude of the oscillations decays exponentially when $c<2$. If it is higher ...
6
votes
1answer
329 views

Physical interpretation: weighted eigenvalues of the Laplacian with a potential

I've already posted this question on Physics.SE, but I thougth it could be useful to ask also here. No problem if moderators will ask me to cancel this thread... But, please, have mercy! :-D Let ...
2
votes
2answers
106 views

Ball from platform with specific vertex

On earth in a vacuum. You throw a platon from a platform height $h$ and want it to land at point $d$ distant. Note, h is absolutely fixed and d is absolutely fixed. It "must land" at point d, no ...
0
votes
1answer
331 views

Acceleration along a 2D plane

It's been a long time since I've done trig, and I never new it very well. I have a problem I don't know how to solve. I have an object on a 2D plane that I want to move. I have this objects x and y ...
8
votes
2answers
811 views

Fireworks under inverse-cube gravity

What is the path of a projectile under an inverse-cube gravity law? Imagine that the law of gravity was changed overnight from $F(r) = G m_1 m_2 / r^2$ to $F(r) = G' m_1 m_2 / r^3$. To be ...
2
votes
2answers
247 views

motion in a straight line

Solution 1 Solution 2 Need to find $a_2$/$a_1$. But I am getting different answers. I found out there can be more solutions other than these two. I am confused why this is happening? Plz Help. ...
0
votes
2answers
956 views

Explain this paradox

Can someone help me explain this paradox please. A simple harmonic oscillator $ma=-kx$ is a system that oscillates in one dimension. But the text book says one-dimensional system can't oscillate. Why ...
1
vote
3answers
3k views

Velocity Question & Acceleration

Below I have a question that I tried to solve on a exam. I am curious as to the actual way to approach the question. What I did was set the equation equal to $0$ and get $t = -3$ then I plugged in $3$ ...
7
votes
2answers
490 views

Studying quantum mechanics without physics background

I am a PhD math student, and I am wondering if I should study quantum mechanics while I don't have an undergrad background in physics. I posted this question in physics stackexchange, but there ...
1
vote
1answer
3k views

How to get angular velocity from difference orientation quaternion and time?

I am using Bullet Physic library to program some function, where I have difference between orientation from gyroscope given in quaternion and orientation of my object, and time between each frame in ...
1
vote
2answers
682 views

Homework help with projectile motion

I would please like help on the following question related to projectile motion. A horizontal drainpipe 6 metres above sea level empties stormwater into the sea. If the water comes out ...