# Tagged Questions

DO NOT USE THIS TAG just because the question contains a differential equation!

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### Minimizing a damping constant in order to minimize the amplitude of oscillations

How can I determine the damping coefficient that minimizes the amplitude of vibrations? This is an extension of Coupled ODEs that model a quad rotor \begin{align} ...
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### What physical phenomena are modelled by Chebyshev equation?

What physical phenomena are modeled by Chebyshev equation? The equation is below $$(1-x^2) {d^2 y \over d x^2} - x {d y \over d x} + p^2 y ~=~ 0 .$$ I could not find it in Wikipedia or in Google (at ...
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### Non-deterministic particle system

This question is in the spirit of Norton's dome, an example of an apparently non-deterministic system in Newtonian mechanics. Under certain restrictions, the Picard–Lindelöf theorem guarantees the ...
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### Describe Ising model dynamics in stochastic differential equation or stochastic process

The Ising model is described by the Hamiltonian $$H(\sigma) = - \sum_{<i~j>} J_{ij} \sigma_i \sigma_j -\mu \sum_{j} h_j\sigma_j,$$ and is treated extensively by equilibrium statistical ...
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Consider a Chern-Simons Lagrangian $\mathscr{L}=\mathbf{e}^2-b^2+g\epsilon^{\mu \nu \lambda} a_\mu\partial _\nu a_\lambda$ in 2+1 dimensions, where the 'electromagnetic' fields are $e_i=\partial _0a_i-... 1answer 198 views ### Is there any physically relevant example of constructing series solution about infinity of an ordinary differential equation? I was reading about how to test if a given second order ordinary differential equation has singularity at infinity from Arfken and Weber. I understood the steps mathematically but I could not find its ... 1answer 371 views ### Differential Equations for Block Diagram of Satellite Attitude Control System I am trying to understand the procedure to setup differential equations from a block diagram. The enclosed example is about the attitude control of a satellite. The ultimate goal is to find a state-... 2answers 163 views ###$R = dV/dI$for varying temperature I'm trying to do my prelab for an E&M course, and am asked if, for plotting$V$vs$I$with a varying temperature, I should expect a linear slope. I know that both$V$and$I$depend on$R$, and ... 2answers 402 views ### Time-dependent Schrödinger equation with$V=V(x,t)I was wondering about the following: If you have the time-dependent Schrödinger equation such that i \hbar \frac{\partial\psi(x,t)}{\partial t} = - \frac{\hbar^2}{2m} \frac{\partial^2\psi(x,t)}{\... 0answers 46 views ### Is there a second order differential wave equation that only allows a finite set of discrete eigenvalues? I tried constructing a second order differential wave equation that only allows a finite set of discrete eigenvalues by using the power series expansion such as \begin{align} A_{j+2} = \dfrac{j-m}{(j+... 1answer 132 views ### Is the mathematical form of the acoustic diffusion equation present in other fields of physics? We are working in the field of High Performance Computing and we have developed a very efficient parallel implementation for solving the Acoustic Diffusion Equation as described below: \frac{\... 2answers 452 views ### What does it mean to “solve an equation”? I don't understand what is meant by there being a "solution" to an equation. For example, what does a solution to the wave or heat equation represent, and what are we solving for? Of course, we can ... 1answer 100 views ### product solutions for PDEs, physical motivation Given a boundary value problem with independent variablesx_1,x_2, \dots , x_n$and a PDE say$U(x_i, y, \partial_j y,\partial_{ij} y, \dots )=0$we typically begin constructing a general solution by ... 1answer 505 views ### Help with Modeling a Liquid Vortex. (Related to General Fusion) I want to model liquid lead swirling in a sphere. This is connected to General Fusion’s fusion machine. A 55 million dollar, Jeff Bezos funded, 60 person company trying to change the world with ... 2answers 158 views ### Why fundamentally does classical mechanics lead to second order dynamics? [duplicate] What's so special about second order equations in classical mechanics? I have a basic understanding of the Lagrangian and Hamiltonian formulations of classical mechanics, so I'm not looking for ... 3answers 270 views ### Solving the simplest coupled nonlinear ODES for chemical kinetics [closed] I am just trying to get the integrated form for the kinetics of the reaction$A + B \rightarrow C + D$characterized by: $$-\dfrac{d[A]}{dt} = -\dfrac{d[B]}{dt} = k[A][B] \; .$$ As you note, ... 1answer 60 views ### Curves satisfying this functional [closed] This is a problem in Hartle's "GRAVITY": Consider the functional $$S[x(t)]= \int_{0}^{T} \left[\left(\frac{dx(t)}{dt}\right)^2 + x^2(t)\right]\text{ }dt$$ Find the curve$x(t)$satisfying the ... 1answer 97 views ### solution of pendulum equation [closed] I have the pendulum expression $$\ddot{\theta}+\omega_{o}^{2}\sin(\theta)=0,$$ where I used a Taylor expansion for the sine term: $$\ddot{\theta}+\omega_{o}^{2}\left(\theta-\frac{1}{6}\theta^3\... 1answer 165 views ### Normal mode of a coupled pendulum: why the constant \psi_1, \psi_2 I need to solve a problem that tells me to find out the motion of both the pendulums that appear in the first 45 seconds of this video I think this kind of motion is described by a system of ... 2answers 185 views ### How do you integrate an expression over a variable in the limit of an integral? I am trying to follow the steps to solve the integro-differential equation that arises from a plasma sheath problem given in this paper. This is the step I can't follow:$$\epsilon_o\frac{d}{d\... 1answer 527 views ### A general solution to continuity equation Let us write the standard continuity equation $$\frac{\partial \rho}{\partial t} + \vec{\nabla} \cdot \vec{\jmath} = 0.$$ Should the relation$\vec{\jmath} = \rho \vec{v}$be considered as a general ... 0answers 41 views ### Is there any general position function$x(t)$that gives the solution to$x''(t) = k/x(t)^2$, where k is a constant? [duplicate] In physics class, I often come across various inverse square law equations like the following:$F_G= G\frac{m_1m_2}{r^2}F_E = k_e\frac{q_1q_2}{r^2}$Specifically, we are typically given ... 2answers 3k views ### First-order wave equation: Why is its presence not common? The (one-dimensional) wave equation is the second-order linear partial differential equation $$\frac{\partial^2 f}{\partial x^2}=\frac{1}{v^2}\frac{\partial^2 f}{\partial t^2}\tag{second order PDE}$$ ... 1answer 146 views ### The source of gravitation in a spacetime without matter In a discussion concerning: Physical meaning of non-trivial solutions of vacuum Einstein's field equations there were a number of answers claiming that the flatness of the Ricci space (Rµv=0) ... 0answers 635 views ### Coupled mass spring system with damping and initial values After researching through the web, I can't figure out how to express into a differential equation a coupled mass spring system with damping and initial values. Two masses and two springs, no external ... 0answers 86 views ### Derivation of cylindrical line heat source problem? I have a line heat source embedded inside a cylinder and I am trying to find the temperature distribution T(r,t). By using the similarity variable, the solution to the differential equation is $$\... 1answer 343 views ### Research problems in application of Lie groups to differential equations [closed] Are there any open problems in physics involving Lie groups and differential equations for a phd theses. Some applications are say, Noether's theorem in classical or quantum field theory. But I am ... 5answers 1k views ### Conservation of Mathematical Constraints when deriving Energy and Momentum from F=ma Background: Starting from F = ma, integrating with respect to time, and using basic calc, one can derive \int Fdt = m (v_f - v_i) Starting from F = ma, integrating with respect to distance, ... 2answers 441 views ### Stick and slip motion: mass and spring inside a box model I am trying to determine a set of differential equation which can describe the motion of a mechanical system as below. Here, at the bottom we have a plate, and a box on top of it. Inside the box, ... 2answers 184 views ### What information is lost in the symmetrization necessary to derive the BBGKY hierarchy? The book on Kinetic theory I'm reading derives the BBGKY hierarchy after introducing the reduced distribution functions f_s(q^1,p_1,q^2,p_2,\dots,q^s,p_s):=\int\ \rho\ \ \mathrm d q^{s+1} \mathrm d ... 1answer 159 views ### Solution of QM tasks by using asymptotics When we solve QM tasks by solving the Schrödinger equation, such as tasks about a particle in a Morse potential, a Poschl-Teller potential and many others, we usually find approximations (lets call ... 1answer 103 views ### Solving 2nd-order ODEs I was reading this PDF REF per request: ... 1answer 82 views ### Showing specififc internal energy e is a perfect differential I am reading a book on Gas dynamics and there is a small section on thermodynamics before the conservation laws of mass momentum and energy are introduced. The book says$$ p = R \rho T$$where$...
Problem: $1.0 \text{ kg}$ of air at pressure $10^6 \text{ Pa}$ and temperature $398 \text{ K}$ expands to a five times greater volume. The expansion occurs such that in every instance the added ...