text stringlengths 81 47k | source stringlengths 59 147 |
|---|---|
Question: <p>Natural phenomena (e.g. heat flow) and systems (e.g. electrical circuits) are usually described using differential equations. Why is that?</p>
<p>Also, usually people use "<em>constant</em> coefficients <em>linear</em> differential equations" of low order (one or two, rarely three). Is this use (... | https://physics.stackexchange.com/questions/349226/why-differential-equations |
Question: <p>I find differential equations in physics to be quite challenging so I'm looking for a book to help me master them.</p>
<p>I'm familiar with solving ordinary differential equations via seperation of variables but haven't really gone much further than that.</p>
<p>I was thinking about buying this: <a href=... | https://physics.stackexchange.com/questions/455312/differential-equations-for-physicists |
Question: <p>We use differential equations to model the world around us. For example, the logistic differential equation
$$\frac{dx}{dt} = rP\left(1-\frac PK\right)$$</p>
<p>is used to model population. However, it doesn't take into account things like climate, natural disasters, competition among other species, etc. ... | https://physics.stackexchange.com/questions/178916/accuracy-of-differential-equations |
Question: <p>I have a system of two Second Order differential equations
$$r^2\ddot{r}−r^3(\dot{\varphi}^2+ω^2)=−GM$$
$$r \ddot{\varphi}+2 \dot{r}(\dot{\varphi}+\omega)=0 $$
using the conserved quantity $(\dot{\varphi}+\omega)r^2$, call it <em>Ω</em>.<br>
I have shown that it is indeed a conserved quantity, as its time-... | https://physics.stackexchange.com/questions/374895/decouple-differential-equations |
Question: <p>Being interested in the mathematical theory, I was wondering if there are up-to-date, nontrivial models/theories where delay differential equations play a role (PDE-s, or more general functional differential equations).</p>
<p>It is clear that</p>
<ul>
<li>in biological (population) models usually pregna... | https://physics.stackexchange.com/questions/27143/applications-of-delay-differential-equations |
Question: <p>We all know recurrence equations like e.q. Fibonacci relation</p>
<p>$$F_{n} = F_{n-1} + F_{n+1}$$</p>
<p>In order to find general expression for any $n$, we can use <em>generating function</em> method </p>
<p>$$G(x) = \sum\limits_{n=0}^{\infty}F_{n}x^{n}$$</p>
<p>or its variation <a href="http://en.wi... | https://physics.stackexchange.com/questions/180701/recurrence-differential-equations |
Question: <p>Why in physics, most of the physical systems are modelled by linear differential
equations?</p>
Answer: <p>I think your qualification of "most" systems needs some clarification because really almost all of the classical universe is described by second-order, nonlinear partial differential equations. Fluid... | https://physics.stackexchange.com/questions/95795/physics-and-linear-differential-equations |
Question: <p>In the book of <span class="math-container">$\textit{The Quantum World of Ultra-Cold Atoms and Light: Book 1 Foundations of Quantum Optics}$</span> by Peter Zoller and Crispin Gardiner on page 75, they derive the phase-amplitude stochastic differential equation for a thermalized oscillator.</p>
<p>From a c... | https://physics.stackexchange.com/questions/757179/phase-amplitude-stochastic-differential-equations |
Question: <p>What is the significance of monodromy matrix in the context of differential equations? I have seen some papers(<a href="http://arxiv.org/abs/1303.6955" rel="nofollow">1</a>,<a href="http://arxiv.org/abs/1403.6829" rel="nofollow">2</a>,<a href="http://arxiv.org/abs/1510.06685" rel="nofollow">3</a> etc) in C... | https://physics.stackexchange.com/questions/238521/monodromy-matrix-and-differential-equations |
Question: <p>As I understand it in QFT interactions are generally modeled as being from the exchange of virtual particles. If I was to think of how to simulate a classical analog I would model two spheres A and B, that each can only change velocity by emitting or absorbing an exchange sphere C. I would use a random n... | https://physics.stackexchange.com/questions/661999/simulating-interactions-in-qft-without-differential-equations |
Question: <p>I understand that if a constraint equation given on a differential form is exact, that means it is also holonomic since I can find a solution. But there are other types of differential equations, like separable and linear, such that I can find an equation in the form of a holonomic constraint. Why is it th... | https://physics.stackexchange.com/questions/370835/exact-differential-equations-and-holonomic-constraints |
Question: <p>As I was thinking about RC circuits it dawned upon me that under the correct configurations one could very efficiently solve differential equations by programming them into an RC circuit (the applications of this would be something like a very very fast hardware implementation of machine learning). </p>
<... | https://physics.stackexchange.com/questions/319285/using-rc-circuits-to-solve-differential-equations |
Question: <p>If I have a differential equations of the form <span class="math-container">$$\frac {d^2y}{dt^2}=\alpha^2y$$</span></p>
<p>Assuming the roots of the characteristic equation is complex the solution to the differential equation is: <span class="math-container">$$y=C_1e^{j\alpha t}+ C_2e^{-j\alpha t}$$</span>... | https://physics.stackexchange.com/questions/643519/solution-to-differential-equation |
Question: <p>I am trying to form a differential equation between two different isotopes, Uranium-238 and Thorium-234.
The rate of decay of an isotope is proportional to the amount present. So that:
<span class="math-container">$$
\frac{dx}{dt} = -kx
$$</span>
Where x is the amount of Uranium-238 and k is the constant... | https://physics.stackexchange.com/questions/550021/radioactive-decay-differential-equations |
Question: <p>Suppose I have a function of time $t$ and position $(x,y)$ such that
\begin{equation} p_t \,dt = p \,dy - p_x (1-x) \,dx + p_y \,dy\end{equation}
where the subscript denotes a differentiation. In this case, I am able to derive a (partial) differential equation from this form.</p>
<p>I'd love to have you... | https://physics.stackexchange.com/questions/52547/from-differentials-to-differential-equations |
Question: <p>While reading this answer by Rishab Navneet <a href="https://physics.stackexchange.com/a/595835/236734">here</a>, it is shown how we can visualize the harmonic oscillator as the shadow of a body moving in a circle onto a line. How was it found that the plane curve is a circle? More generally, is there a wa... | https://physics.stackexchange.com/questions/595945/shadow-method-of-solving-differential-equations |
Question: <p>In my physics class we learned the equations for self-induction. Our teacher also showed us the differential equations and gave us the solutions. Because we didn't have differential equations in our Maths class he only told us that, if we were interested in how to solve these equation, we should look up se... | https://physics.stackexchange.com/questions/356130/solving-the-differential-equations-for-self-induction |
Question: <p>What is the importance of finding new exact solutions to partial differential equations? I kindly need someone to convince me, since my PhD will be on that. </p>
Answer: <p>If you have an analytical/exact (in contrast to some say "discretized" or similar numerical) solution, interpretation of the coeffici... | https://physics.stackexchange.com/questions/513007/significance-of-exact-solutions-to-differential-equations |
Question: <p>I'm trying to simulate a real system, in order to do so I have modelled a physical system (fluid-mechanical) that behaves similarly with some simplifications. The physical model in question is as follows:</p>
<p><a href="https://i.sstatic.net/CP1Sf.png" rel="nofollow noreferrer"><img src="https://i.sstati... | https://physics.stackexchange.com/questions/294572/differential-equations-of-a-fluid-mechanical-system |
Question: <p>I'm trying to find the equation for a ball thrown from the ground with an initial velocity. Are these differential equations correct? I solved these and set the integrating constant to $v_0cos(\theta)$ for $v_x$ and $v_0sin(\theta)$ for $v_y$ and integrated again to get the function of position. Is that th... | https://physics.stackexchange.com/questions/317293/differential-equations-ball-with-air-resistance |
Question: <p>Is there a way to show that the motion of Earth around the Sun is elliptical (<a href="https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion" rel="nofollow noreferrer">Kepler's 1st law</a>) from Newton's laws without resorting to the use of differential equations of motion?</p>
Answer: <p>Newt... | https://physics.stackexchange.com/questions/86435/proving-keplers-1st-law-without-differential-equations |
Question: <p>Wikipedia says about the equations of motion that;</p>
<blockquote>
<p>"If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics."</p>
</blockquote>
<p>And</p>
<blockquote>
<p>"A differential equation of motion... | https://physics.stackexchange.com/questions/606669/does-the-suvat-equations-of-motion-kinematics-come-from-some-differential-equa |
Question: <p>I was just messing around with Newton's Law of gravitation, when I had the idea of converting Newton's Law into differential form (more or less like Maxwell's equations).</p>
<p>I did the following:</p>
<h5>#1 Divergence of the field:</h5>
<p><span class="math-container">$$
\iint_C {\mathbf g \cdot d\mathb... | https://physics.stackexchange.com/questions/710179/gravity-differential-equations |
Question: <p>I am building simulation using differential equations to model the motion of a damped vertical spring-mass system. I wish to use this simulation to extract data. For example, I am trying to find the effect of mass on the damping. </p>
<p>The problem I am facing is every time I run the model, I receive the... | https://physics.stackexchange.com/questions/519857/building-realistic-simulation-using-differential-equations |
Question: <p>I know many of you are tired of book recommendation posts and questions. But I am self learning Theoretical Physics, and I am having a hard time choosing a book to learn differential equations (ODEs). I really want a good understanding of differential equations; I have been told that ODEs and PDEs are the ... | https://physics.stackexchange.com/questions/571726/looking-for-a-good-book-on-differential-equations |
Question: <p><img src="https://i.sstatic.net/zuU5y.png" alt="Text Book Cut Out"></p>
<p>I am trying to understand the procedure to setup differential equations from a block diagram. The enclosed example is about the attitude control of a satellite. The ultimate goal is to find a state-space system representation of th... | https://physics.stackexchange.com/questions/122219/differential-equations-for-block-diagram-of-satellite-attitude-control-system |
Question: <p>Are there any open problems in physics involving Lie groups and differential equations for a phd theses. </p>
<p>Some applications are say, Noether's theorem in classical or quantum field theory. But I am not sure if those topics lead to any research problems. </p>
<p>So any idea about prospective resear... | https://physics.stackexchange.com/questions/100800/research-problems-in-application-of-lie-groups-to-differential-equations |
Question: <p>In physics, many problems start with a mathematical relationship of the physical phenomenon at hand, and then, in many occasion, always only leave whatever in the first order to get a nice and solvable differential equation. Then there may be terms of higher order considered later, by as far as I know, it ... | https://physics.stackexchange.com/questions/133974/solving-differential-equations-without-approximations |
Question: <p>A quantum field is an operator valued function, that is, a function $\varphi(x)$ defined on spacetime which assigns operators on a Hilbert space to each event $x$. In a more rigorous approach a quantum field could be defined as an operator valued distribution on spacetime.</p>
<p>Anyway, it is quite commo... | https://physics.stackexchange.com/questions/320114/how-to-make-sense-of-quantum-fields-differential-equations |
Question: <p>From <a href="https://doi.org/10.1063/1.2155755" rel="nofollow noreferrer">https://doi.org/10.1063/1.2155755</a></p>
<blockquote>
<p>he limited himself to second-order differential equations.</p>
</blockquote>
<blockquote>
<p>Our experience in elementary-particle physics has taught us that any term in the ... | https://physics.stackexchange.com/questions/679352/higher-order-derivatives-than-second-order-differential-equations |
Question: <p>I've studied the basic concepts of partial differential equations, and one question comes to my mind. What are the propuse of the diferent methods of resolution of differential equations. For example if you start with:
<span class="math-container">$$
\frac{1}{c^2}\frac{\partial^2 \Psi}{\partial t^2} - \fra... | https://physics.stackexchange.com/questions/778559/on-different-methods-of-solving-differential-equations |
Question: <p>We found some interesting insights in differential equations of the form</p>
<p>$y^{(n)}(x)+F_\lambda(y(x),y'(x),...,y^{(n-1)}(x))=0$,</p>
<p>i.e. for ordinary differential equations of $n$-th order with $n\geq2$. The function $F$ is polynomial which can include a set of parameters $\lambda$.</p>
<p>We ... | https://physics.stackexchange.com/questions/283292/application-for-differential-equation-of-higher-order |
Question: <p>I am trying to solve the following differential equation;</p>
<p><span class="math-container">$$\frac{d^2 x}{d t^2}=-\omega^2 x \delta(t-t^\prime).$$</span></p>
<p>I know this is of the form</p>
<p><span class="math-container">$$x(t)= A \sin(\omega t) + B \cos(\omega t).$$</span></p>
<p>However this delta ... | https://physics.stackexchange.com/questions/575708/differential-equation |
Question: <p>I have heard from my physics teacher that differential equations are very useful in physics. In what parts of physics exactly is it useful? Why are they generally useful?</p>
Answer: <p>I'd like to elaborate on an earlier answer.</p>
<p>In general the quantities that go into the equations come in chuncks,... | https://physics.stackexchange.com/questions/733203/why-are-differential-equations-used-a-lot-in-physics |
Question: <p>In the <a href="https://www.feynmanlectures.caltech.edu/I_23.html" rel="nofollow noreferrer">twenty third Feynman lecture</a>, the solution of the following differential equation is discussed:</p>
<p><span class="math-container">$$ \frac{d^2 x}{dt^2} + \frac{kx}{m} = \frac{F}{m}$$</span></p>
<p>AFter 'comp... | https://physics.stackexchange.com/questions/623561/complex-exponential-method-of-solving-differential-equations |
Question: <p>What forms of differential equations have numerical solutions with errors that go to zero with sufficient computational power? For example, suppose I want to solve a differential equation <span class="math-container">$E$</span> for a position vector <span class="math-container">$r$</span> at time <span cla... | https://physics.stackexchange.com/questions/815292/numerical-solution-of-differential-equations-e-g-the-three-body-problem |
Question: <p>In my differential equations course an example is given from the Lotka-Volterra system of equations:</p>
<p>$$ x'=x-xy$$</p>
<p>$$y'=-\gamma y+xy.\tag{1}$$</p>
<p>This is then transformed by the substitution: $q=\ln x, p=\ln y$. </p>
<p>$$ q'=1-e^p$$</p>
<p>$$p'=-\gamma +e^q.\tag{2}$$</p>
<p>Then wit... | https://physics.stackexchange.com/questions/249567/hamiltonian-from-a-differential-equation |
Question: <p>How to solve the following differential equation with tensor indices?</p>
<p><span class="math-container">$\epsilon_{\mu\nu}\partial^{\gamma}\partial_{\gamma}f-2i\epsilon_{\mu\nu}p.\partial f+ip_{\mu}x^{\gamma}\epsilon_{\nu\gamma}+ip_{\nu}x^{\gamma}\epsilon_{\mu\gamma}-i(p.x)\epsilon_{\mu\nu}+2\epsilon_{\m... | https://physics.stackexchange.com/questions/822202/tensor-differential-equation |
Question: <p>Consider the following dynamically coupled two state hamiltonian, $$H=-B\sigma_z-V(t)\sigma_x.$$Taking the eigenfunctions of $\sigma_z$ ($|+>$ and $|- >$) as basis vectors, we have the wave function to be $$\Phi=c_
1|+>+ c_2|->$$ and we get coupled differential equations for the time evolution ... | https://physics.stackexchange.com/questions/252692/decoupling-coupled-differential-equations-in-dynamically-coupled-two-state-syste |
Question: <p>I have a question which states</p>
<blockquote>
<p>An astronaut is conducting an experiment on a spaceship under conditions of zero gravity. A bead is threaded on a circular wire, and set in motion with angular velocity $ \omega _0 $ about the centre. If the coefficient of friction between the bead and ... | https://physics.stackexchange.com/questions/359220/differential-equation-in-non-uniform-circular-motion |
Question: <p>I'm sometimes mystified by the use of differentials in physics. I don't understand which formulas—on which occasions—can be thought of as differential equations and which cannot.</p>
<p>While discussing work done by a piston during an isothermal process, my textbook does not treat <span class="math-contain... | https://physics.stackexchange.com/questions/614395/how-do-i-know-which-equations-can-be-treated-as-differential-equations-and-which |
Question: <p>I have only ever seen the Schrodinger equation for the hydrogen atom written out in a form like this:
$$
-\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \psi}{\partial r}\right) + \frac{1}{r^2\sin{\theta}}\frac{\partial}{\partial \theta}\left(\sin{\theta}\frac{\pa... | https://physics.stackexchange.com/questions/141238/rewriting-the-hydrogen-schrodinger-equation-as-a-system-of-differential-equation |
Question: <p>I have a question regarding Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973), Gravitation ISBN 978-0-7167-0344-0. It is a book about Einstein's theory of gravitation.</p>
<p>In page 166 of chapter 6.2 about Hyperbolic Motion, the authors present a person feeling constant acceleration <sp... | https://physics.stackexchange.com/questions/488335/relativity-and-differential-equation |
Question: <p>On article "On the dimensionality of spacetime (<a href="https://space.mit.edu/home/tegmark/dimensions.pdf" rel="nofollow noreferrer">https://space.mit.edu/home/tegmark/dimensions.pdf</a>) Max Tegmark writes about ultrahyperbolic differential equations leading to unpredictability:</p>
<blockquote>
<p>... | https://physics.stackexchange.com/questions/836427/multiple-time-dimensions-and-understanding-ultrahyperbolic-differential-equation |
Question: <p>I have read that the Einstein Field Equations (<a href="http://en.wikipedia.org/wiki/Einstein_field_equations" rel="nofollow">http://en.wikipedia.org/wiki/Einstein_field_equations</a>) can be expressed as a series of differential equations. Some say 16, others say 10 (The disparity seems to stem from a si... | https://physics.stackexchange.com/questions/189515/what-is-the-partial-differential-equation-expansion-of-the-einstein-field-equati |
Question: <p>The second order differential equations are time reversible. That means: they don't distinguish the time arrow direction. There is no reason for the time to flow forward. </p>
<p>My professor told me that there are two solutions to such equations, one of which describes processes going forward and one bac... | https://physics.stackexchange.com/questions/323233/how-second-order-differential-equations-do-not-violate-causality |
Question: <p>I am having troubles deriving the 2nd order differential equation for the system below, where $r=y-s$. According to my lecture notes the differential equation is</p>
<p>$$
M\frac{d^2r}{dt^2}+b\frac{dr}{dt}+kr=-M\frac{d^2s}{dt^2}=-Ma \\
\ddot r+2\zeta \omega_0 \dot r+\omega_0² r=-a,
$$</p>
<p>whereas $ \... | https://physics.stackexchange.com/questions/317718/differential-equation-for-an-accelerometer |
Question: <p>Suppose you have a set of differential equations that you wish to normalize/make dimensionless. From what I've seen, you can usually use dimensional analysis to figure out a good choice of constants to make your variables and parameters dimensionless. However, in fluid dynamics, for example, you also have ... | https://physics.stackexchange.com/questions/446939/general-question-about-making-differential-equations-dimensionless |
Question: <p>Currently working on a problem and I can really figure out how to write the differential equations for it. Here's the situation:</p>
<p><a href="https://i.sstatic.net/O1WAM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/O1WAM.png" alt="Image of the system" /></a></p>
<p>So we have a mass <s... | https://physics.stackexchange.com/questions/615333/differential-equations-of-a-forced-coupled-spring-pendulum-system |
Question: <p>With friend, we are writing an interactive educational simulation of particle falling into a black hole. </p>
<p>Currently we use <a href="http://en.wikipedia.org/wiki/Schwarzschild_geodesics#Geodesic_equation">Schwarzschild geodesics</a>. However, we want to generalize it to the case of <a href="http://e... | https://physics.stackexchange.com/questions/43629/kerr-geodesics-differential-equations-in-equatorial-plane |
Question: <p>Suppose that we are given the Schwarzschild metric and its Lagrangian <span class="math-container">$L=-(1-\frac{R}{r})t'^2 + (1-\frac{R}{r})^{-1}r'^2+r^2 \theta'^2+r^2 \sin^2(\theta)\phi'^2$</span> where R=<span class="math-container">$r_s=2GM$</span> and <span class="math-container">$x'=\frac{d}{d \tau}$... | https://physics.stackexchange.com/questions/675913/schwarzschild-metric-system-of-geodesic-differential-equations |
Question: <p>Could it happen than a solitary travelling wave (soliton) had a different propagation speed when seen from the usual wave equations from that in a non-linear equation. I mean, suppose a solution <span class="math-container">$F=f(x-vt)+g(x+vt)$</span> of the usual wave equation.</p>
<p>Could it happen than ... | https://physics.stackexchange.com/questions/750453/wave-propagation-speed-in-non-linear-differential-equations |
Question: <p>In a chapter on oscillations in <a href="https://openstax.org/books/university-physics-volume-1/pages/15-4-pendulums" rel="noreferrer">a physics book</a>, the differential equation <span class="math-container">$$\ddot{\theta}=-\frac{g}{L}\sin(\theta)$$</span> is found and solved using the small-angle-appro... | https://physics.stackexchange.com/questions/653845/solution-to-pendulum-differential-equation |
Question: <p>In Birrel & Davies: <em>QFT in curved spacetime</em> it is written that the following differential equation can be solved in terms of hypergeometric functions.
$$(\partial_t^2 +(k^2+c(t)m^2))\phi(t)=0.$$
But there is no reference and no method listen.
Could somebody please help me solve this equation f... | https://physics.stackexchange.com/questions/299251/hypergeometric-function-differential-equation |
Question: <p>I apologize ahead of time, in case this post is not allowed. </p>
<p>After taking a few courses at a community college, I've taken the fall 2013 semester off (I was accepted into a university for the spring 2014 semester). I'm really looking to spend the next 5 months on concentrated self-study to be a bi... | https://physics.stackexchange.com/questions/75506/differential-equations-waves-physics-self-study-suggestions |
Question: <p>Since we don't know whether space and time are discrete or continuous wouldn't it be a better idea to use $h$-difference equations where the derivative is $$f'(x) =\frac{f(x+h)-f(x)}{h},$$ since they are more general and by sending $h$ to 0, we would have the usual differential equations. So why do we pref... | https://physics.stackexchange.com/questions/369481/why-do-we-use-differential-equations-in-physics-instead-of-h-difference-ones |
Question: <p>I'm trying to derive the rocket equation.</p>
<p>I'm pretty sure that the differential equation for the rocket equation is</p>
<p><span class="math-container">$$v(t)\delta t =\frac{m(t)\delta t }{m(t)} V_e$$</span></p>
<p>where </p>
<ul>
<li><span class="math-container">$v(t)\delta t$</span> is the rat... | https://physics.stackexchange.com/questions/449027/solving-the-rocket-differential-equation |
Question: <p>Suppose I begin with the time-independent Schrodinger equation
$$ \left(-\frac{1}{2m}\partial_x^2 + V(x)\right)\psi_n(x) = E_n\psi_n(x), $$
ordinarily we specify the function $V$ and then solve for a set of eigenfunctions and eigenvalues. And just to be slightly more general, we do the same thing with Stu... | https://physics.stackexchange.com/questions/190164/constructing-differential-equation-from-arbitrary-hamiltonian |
Question: <p>I'm solving the velocity profile of a fluid flow for a circular channel with an oscillating pressure gradient <span class="math-container">$\frac{dp}{dx}=\frac{\Delta p}{\rho L}e^{-i\omega t}$</span>. I plugged in to the Navier Stokes equations and am having trouble figuring out how to approach the solutio... | https://physics.stackexchange.com/questions/534832/trouble-solving-partial-differential-equation |
Question: <p>In Landau–Lifshitz's <em>Course of Theoretical Physics</em>, Vol. 2 (‘Classical Fields Theory’), Ch. IV, § 27, there is an explanation why the field equations should be linear differential equations. It goes like this:</p>
<blockquote>
<p>Every solution of the field equations gives a field that can exist i... | https://physics.stackexchange.com/questions/13466/why-must-the-field-equations-be-differential |
Question: <p>The Schrödinger equations have the term $\Psi$, which is the wave function.</p>
<p><a href="http://scienceworld.wolfram.com/physics/SchroedingerEquation.html" rel="nofollow noreferrer">http://scienceworld.wolfram.com/physics/SchroedingerEquation.html</a></p>
<p>I do not know what type of equation the wav... | https://physics.stackexchange.com/questions/416260/is-the-%ce%a8-in-the-schr%c3%b6dinger-equation-the-same-as-the-%ce%a8-in-exact-equations-fi |
Question: <p>I've been asked to find a partial differential equation that has applications in material science. However we are not allowed to use the heat equation. I have found Fick's laws (basically the heat equation), and the Schrodinger equation, but I was wondering if there were any other prominent applications in... | https://physics.stackexchange.com/questions/160332/applications-of-partial-differential-equations-in-material-science |
Question: <p>I have read at this site as an answer at a question about how antennas work but that is not important</p>
<p>The resonant frequency of an antenna is determined by its constitution. Mathematically speaking, this is a general property of second order differential equations but in down-to-earth terms any AC c... | https://physics.stackexchange.com/questions/749963/is-resonance-a-general-property-of-second-order-differential-equations |
Question: <p>The following series of differential equations represents a projectile's path when solved (g=9.81):</p>
<p><img src="https://i.sstatic.net/1gXIu.png" alt="The system"></p>
<p>Here is some sample output from this system (with initial values x,y=0, v=1500, theta=1.33):</p>
<p><img src="https://i.sstatic.n... | https://physics.stackexchange.com/questions/175197/modifying-differential-equations-representing-a-projectile-system-to-account-for |
Question: <p>This may be a stupidly obvious question, but can multiple forces (such as acceleration due to gravity and air resistance acting on a falling object) be expressed algebraicly or must it be written in the form of a differential equation? Since I don't know much about differential equations I have struggled ... | https://physics.stackexchange.com/questions/262473/must-multiple-forces-be-expressed-as-a-differential-equation |
Question: <p>I am just an independent student and was learning thermal expansion with differential equations and i saw someone on the internet solving the differential equation for the law like below:</p>
<p><span class="math-container">$$\frac{1}{L}\frac{dL}{dT}=\alpha$$</span>
<span class="math-container">$$\int_{L_{... | https://physics.stackexchange.com/questions/814191/why-can-you-integrate-with-different-bounds-in-thermal-expansion-differential-eq |
Question: <p>I am looking for a differential equation whose solutions are what I call "open" vortices.
These vortices are not closed in themselves, but sort of "absorb" the surrounding "fluid" and also "emit" it.
I know that the Gross–Pitaevskii equation has vortices as solutions, but these are closed vortices as far a... | https://physics.stackexchange.com/questions/400029/vortex-solution-to-differential-equation |
Question: <p>Consider a system of two coupled linear differential equations
<span class="math-container">$$
\left(
\begin{bmatrix}
\Omega
\end{bmatrix}^{-1}
+ \frac{d^2}{dt^2} \right)
\vec{V}(t)
=
\begin{bmatrix}
C
\end{bmatrix}^{-1}
\vec{J}(t)
+ \begin{bmatrix}
\Omega
\end{bmatrix}^{-1} \vec{K}(t)
$$</span... | https://physics.stackexchange.com/questions/545343/lagrangian-for-two-coupled-second-order-linear-differential-equations |
Question: <p>Is there a numerical algorithm for solving a pair of coupled second order differential equations?</p>
<p>This question arises from a homework problem that I have that involves two dimensional projectile motion. The problem is as follows:</p>
<blockquote>
<p><em>An object is fired through a viscous flui... | https://physics.stackexchange.com/questions/100368/numerical-solution-of-two-coupled-second-order-differential-equations-of-motion |
Question: <p>I would be very grateful if someone could tell me something about the following partial differential equation:</p>
<p>$$
\frac{\partial U}{\partial t} = K * (\frac{\partial^2 U}{\partial r^2} + (1/r)\frac{\partial U}{\partial r}).
$$</p>
<p>A friend told me that the equation models the <a href="http://e... | https://physics.stackexchange.com/questions/192341/help-recognizing-partial-differential-equation |
Question: <p>The differential equation of an anharmonic Oscillator with Newtonian friction is
<span class="math-container">$$
\ddot{x}+\varepsilon \dot{x}^2+x=0
.$$</span>
The initial conditions of the System are
<span class="math-container">$$
\begin{align*}
x(0)&=1\\
\dot{x}(0)&=1
.\end{align*}
$$</span>
The... | https://physics.stackexchange.com/questions/774534/solving-differential-equation-in-perturbation-theory |
Question: <p>I want to solve the equations of motion for a system with a unit step function. Are there any methods that can be used to solve these? As a toy model, I picked a sliding mass bouncing off a spring.
The setup for the problem is:
<span class="math-container">$$mx''= -\Theta(x)kx \\ x(0)=u \qquad u > 0 \\ ... | https://physics.stackexchange.com/questions/810499/differential-equation-with-step-function |
Question: <p>Let the radiation absorbed by a material be given as a function <span class="math-container">$N(x)$</span>, where <span class="math-container">$x$</span> is the material's layer thickness. In a piece with a thickness of <span class="math-container">$dx$</span>, <span class="math-container">$dN$</span> part... | https://physics.stackexchange.com/questions/673412/differential-equation-for-radiation-absorption |
Question: <p>Light is a self-propagating wave, but it's very complicated.</p>
<p>Imagine, if you will, a wave in space-time that by assumption was self-propagating like light, except that it was a <a href="https://en.wikipedia.org/wiki/Gravitational_wave" rel="nofollow noreferrer">gravitational wave</a>.</p>
<p>What ar... | https://physics.stackexchange.com/questions/704462/what-are-the-differential-equations-that-model-a-self-propagating-gravitational |
Question: <p>I have been studying differential equations in RLC circuits: specifically I am looking at </p>
<p><strong><em>a generator with fixed EMF $=E$,<br>a capacitor $C$, <br>an inductor with inductance $L$ and internal resistance $r$,<br> and a separate resistor $R$</em></strong> </p>
<p>with the elementary cas... | https://physics.stackexchange.com/questions/112713/specific-differential-equation-in-rlc-circuit |
Question: <p>I am currently reading Griffiths, 'Introduction to Electrodynamics', 3rd ed, Chapter 10.1.3, the section on Gauge Invariance, and was reached a point of confusion. In particular, the differential equations that arose from choosing the Coulomb gauge $\nabla \cdot \vec{A}=0$:</p>
<p>$$\nabla^2 V=-\frac{1}{\... | https://physics.stackexchange.com/questions/307845/confusion-about-coulomb-gauge-differential-equations-for-veca-and-v |
Question: <p>Please consider the following RC circuit as context:</p>
<p><a href="https://i.sstatic.net/o0gAI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/o0gAI.png" alt="enter image description here"></a>
Assume that the circuit has been connected for a long time. If switch S has been opened at <spa... | https://physics.stackexchange.com/questions/556163/differential-equations-in-a-discharging-rc-circuit-in-parallel |
Question: <p>In order to determine the geodesics, one must solve the following set of differential
equations
\begin{align}
\frac{d^2 x^j}{ds^2} + {j\brace h\,\,k}\frac{dx^h}{ds}\frac{dx^k}{ds} = 0,
\end{align}
where ${j\brace h\,\,k}$ is the Christoffel symbol of second kind, which is defined as
\begin{align*}
{j\bra... | https://physics.stackexchange.com/questions/220298/existence-of-a-solution-for-geodesic-differential-equations-for-a-singular-metri |
Question: <p><a href="https://i.sstatic.net/4hemJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/4hemJ.png" alt="enter image description here"></a></p>
<p>From the constraint <span class="math-container">$v=a\dot{\phi}$</span> of a rolling disk over a plane, where <span class="math-container">$a$</span... | https://physics.stackexchange.com/questions/482949/non-integrable-differential-equation-and-non-holonomic-contraints |
Question: <p>One can write down the solution of a linear stochastic differential equation in Ito convention of the form
<span class="math-container">$$
d\vec{x} = F\vec{x}dt+G\vec{x}dW
$$</span>
where <span class="math-container">$G,F$</span> are constant matrices and <span class="math-container">$dW$</span> is a Wiene... | https://physics.stackexchange.com/questions/842189/solution-of-quadratic-stochastic-differential-equation |
Question: <p>Let's say we have an equation of the form</p>
<p><span class="math-container">\begin{equation}
\nabla _\vec{u}u^\mu(\tau)=F^\mu\big[x(\tau)\big]
\end{equation}</span></p>
<p>The operation on the left hand side is the usual covariant derivative along the worldline</p>
<p><span class="math-container">\begin{... | https://physics.stackexchange.com/questions/763593/integrating-differential-equations-in-general-relativity |
Question: <p>In General Relativity, when we are obtaining the Schwarzchild solution, we get from Einstein's equation three differential equations but only two unknown functions [A(r) and B(r)]:</p>
<p><span class="math-container">$R_{00}=-\frac{A''}{2B}+\frac{A'}{4B}\left(\frac{A'}{A}+\frac{B'}{B}\right)-\frac{A'}{rB}=... | https://physics.stackexchange.com/questions/620661/number-of-differential-equations-and-unknown-functions-in-spherically-symmetric |
Question: <p>Can you please help me in modelling a circuit using the differential equation? In the following equation, $u(t)$ is the input voltage and $y(t)$ is the output voltage.</p>
<p>$$y(t)=2u(t)+3\frac{du(t)}{dt}+4\int_0^tu(t)dt.$$</p>
<p>How do I draw a circuit such that the input voltage $u(t)$ and the output... | https://physics.stackexchange.com/questions/77258/drawing-the-circuit-from-a-differential-equation |
Question: <p>I tried to solve an exercise related to Schwarzschild metric, and at some point found next question <a href="https://physics.stackexchange.com/q/620576/">Question</a></p>
<p>I can't figure out how the first line turns out.</p>
<blockquote>
<p>With studying Schwarzschild metric geodesics one can easily come... | https://physics.stackexchange.com/questions/837660/differential-equation-from-schwarzschild-metric |
Question: <p>I'm a second-year undergrad and currently taking a course in Mathematical Physics which covers the topics of Dirac delta functions, Fourier series, Fourier transforms and Differential equations. They recommended using Boas' "Mathematical Methods in Physical Sciences" book. However, I find the book too "wis... | https://physics.stackexchange.com/questions/518442/book-recommendations-for-fourier-series-dirac-delta-function-and-differential-e |
Question: <p>I am teaching differential equations and I got myself totally confused about the physics of a problem.</p>
<p>Consider a coupled spring system in series: there is a mass $m_1$ on a horizontal track which is connected to a wall by a spring (with natural length $L_1$ and spring constant $k_1$). Also attach... | https://physics.stackexchange.com/questions/392542/understanding-the-terms-in-coupled-springs-differential-equation |
Question: <p>I know how to use Buckingham Pi Theorem to, for example derive from the functional equation for a simple pendelum, with the usual methods also described <a href="https://projects.exeter.ac.uk/fluidflow/Courses/FluidDynamics3211-2/DimensionalAnalysis/dimensionalLecturese4.html" rel="nofollow">here</a></p>
... | https://physics.stackexchange.com/questions/273711/dimensional-analysis-in-differential-equations |
Question: <p>I tried to solve a differential equation, but unfortunately got stuck at some point. </p>
<p>The problem is to solve the diff. eq. of hard clamped on both ends rod.
And the force compresses the rod at both ends.
the solution(v(x)) is the value of bending I need.</p>
<p>I assuming, that the differential... | https://physics.stackexchange.com/questions/40885/a-differential-equation-of-buckling-rod |
Question: <p>Let's consider the following: </p>
<blockquote>
<p>We have a Green function <span class="math-container">$G$</span>, and we want to know what linear differential equation is solved by <span class="math-container">$G$</span>. </p>
</blockquote>
<p>How to do this? The question is: If I know <span class="... | https://physics.stackexchange.com/questions/496283/search-for-differential-equation-from-green-function |
Question: <p>I am working through <em>Nonlinear Dynamics and Chaos</em> by Steven H Strogatz. In chapter 3.5 (overdampened beads on a rotating hoop), a differential equation is converted into a dimensionless form. I am trying to work out which dimensions the initial equations had, and why the converted form is dimensio... | https://physics.stackexchange.com/questions/521952/dimensionless-expression-for-differential-equation |
Question: <p>I try to follow the derivation of Rabi two-level problem but I went into trouble when attempting to set up the equations as many notes have suggested.</p>
<p>Using the book (Laser cooling and trapping by Metcalf and Straten) I am reading. We start by with writing down Schrodinger's equation for a two-leve... | https://physics.stackexchange.com/questions/388677/setting-up-differential-equations-for-two-level-rabi-problem |
Question: <p>I encountered the following statement in Boyce's <em>Elementary Differential Equations and Boundary Value Problems</em> : </p>
<blockquote>
<p>Not all differential equations have solutions; nor is the question of existence purely mathematical. If a meaningful physical problem is correctly formulated mat... | https://physics.stackexchange.com/questions/354051/should-every-physical-problem-formulated-as-a-differential-equation-have-a-mathe |
Question: <p>I'm doing some self-study on physics and came across this problem:</p>
<blockquote>
<p>A disk rolls without slipping across a horizontal plane. The plane of the disk remains vertical, but it is free to rotate about a vertical axis. What generalized coordinates may be used to describe the motion? Write a di... | https://physics.stackexchange.com/questions/732826/differential-equation-for-describing-a-moving-disk |
Question: <p>I am trying to reproduce some results from a paper
<a href="https://iopscience.iop.org/article/10.1209/epl/i1998-00235-7" rel="nofollow noreferrer">https://iopscience.iop.org/article/10.1209/epl/i1998-00235-7</a></p>
<p>The authors solved a 4th order partial differential equation
<span class="math-containe... | https://physics.stackexchange.com/questions/839455/frobenius-method-for-fourth-order-differential-equation |
Question: <p>I am currently reading up on Maxwell's Equations (specifically Ampere's Circuital Law- with Maxwell's Addition) for a presentation on differential equations.</p>
<p>I chose the topic ignorant of how the differential form of these equations are used, and I cannot seem to find a digestable use of their diff... | https://physics.stackexchange.com/questions/466189/how-are-the-differential-forms-for-maxwells-equations-used |
Question: <p>I have two questions about the picture.</p>
<p>1)
I think classical propagator itself is not function, is just an operator.</p>
<p>And "(operator)(function)" is not that "(operator)X(function)".</p>
<p>So it seems that the product rule can't be applied in differentiation.</p>
<p>Then, i... | https://physics.stackexchange.com/questions/816994/is-it-possible-that-classical-propagator-be-used-as-an-integrating-factor-for-so |
Question: <p>(I originally posted this on math stack exchange but was advised to post it here)</p>
<p>I am considering the following boundary value problem:
$$-\frac{\mathrm{d}}{\mathrm{d}x} \left[ a(x) \frac{\mathrm{d}}{\mathrm{d}x}(u(x)) \right] + c(x)u(x) = f(x),$$
where $x \in [0,1]$ and $u(0) = u(1) = 0.$</p>
<... | https://physics.stackexchange.com/questions/371393/physical-meaning-of-this-boundary-value-differential-equation |
Question: <p>I am working on the paper titled "Energetic and entropic effects of bath-induced coherences" (<a href="https://arxiv.org/abs/1905.02013" rel="nofollow noreferrer">https://arxiv.org/abs/1905.02013</a>)and there is a two parameter differential equation for calculating the population rates such that... | https://physics.stackexchange.com/questions/810734/two-parameter-differential-equation-solution |
Question: <p>I am working in extensions of General Relativity Theory and at the moment of taking the Newtonian limit of this extension theory (essentialy, mathematically speaking, this is just linearizing the field equations obtained via the variational principle, but this is not important) I arrive to the following pa... | https://physics.stackexchange.com/questions/582593/trouble-solving-partial-differential-equation-with-laplacian-squared |
Question: <p>I am currently working on problem in my own research. There seems to be a weak analogy between my problem and motion on a spring. Therefore, I am exploring this question in regards to a mass oscillating on a spring in hopes to gain further insight into my own system in question.</p>
<p>Here is the idea: W... | https://physics.stackexchange.com/questions/406265/amplitude-of-oscillation-without-solving-differential-equation |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.