Questions tagged [equations-of-motion]

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Test charge in 2+1 dimensions

Given a Chern-Simons theory,as in this resource(page 4), in 2+1 dimensions we can define the electric and magnetic fields as $$ E_i=-\partial_iA_0-\partial_0A_i\;\;\;B=\epsilon^{ij}\partial_iA_j $$ ...
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What is the difference between equation of motion, equation of change and momentum equation in transport phenomena?

What is the difference between equation of motion, equation of change and momentum equation in transport phenomena?
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Equations of Motion and Minimization of Spacetime Interval

I'm trying to show that the extrema of a path in spacetime, as given by the spacetime interval (or length if just considering space) is the one that solves the equations of motion. Let a path be given ...
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Relation between equations of the form "Derivative" $f=0$

I'm currently taking an introductory course in QFT, and I've noticed that lots of equations in physics take the form of "Derivative" of a funcition equal 0. Some examples being the wave ...
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Euler-Lagrangian equation of motion of quantum fields in QFT

A canonical way of doing quantum field theory is by starting with some Lagrangian, for example, that of free scalar field $$L=\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi-\frac{1}{2}m\phi^2$$ Then ...
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What is the difference between 'Equation of motion' and 'Transport equation'?

I think this is a simple question with a not so easily explained answer. What is the difference between the Equation of motion and Transport eq? Is Navier stokes equation an 'Equation of motion' or a '...
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Paradox in the Kinematic Equations of Motion

The 5 equations of motion have been chosen such that from the 5 variables of motion: $s$, $u$, $v$, $a$ and $t$; each equation, exclusively omits one of these. This allows us to only ever require the ...
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Equations of motion of the metric in Classical Dilaton Gravity

In these lecture notes by Strominger section 3.3 we derive the equations of motion of the Classical Dilaton Gravity action $$ S = \frac{1}{2\pi}\int{d^2x}{\sqrt{-g}e^{-2\phi}\left(R +4 (\nabla\phi)^2+...
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Heisenberg's equation of motion without reference to Schrödinger's picture

Well I'm reading Mukhanov & Winitzki's Introduction to quantum effects in gravity, and I got to the exercise 2.8 that ask to derive Heisenberg's equation of motion \begin{equation} \frac{d\hat{A}}{...
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Can energy conservation equation be seen as equation of motion?

After all, energy conservation equation is a differential equation that can be solved to find the motion, but this is never done. It is alway considered equation of motion only the time derivative of ...
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Why do we need to equation of state (EOS) equation?

I cannot understand why we need the equation of state of star for the numerical solution of TOV equation. In fact, I do not know how EOS equation helps with solving TOV equation. How is EOS equation ...
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Newton-Euler approach for the equations of motion of spherical pendulum attachted to a moving body with 6 degrees of freedom

I would like to obtain equations of motion for a spherical pendulum suspended from a (6 degrees of freedom) moving body (generalization of a simple pendulum on a cart) using Newton-Euler approach. ...
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Trajectory of magnetic dipole in a inhomogeneous magnetic field

Goal: I want to use Python to illustrate how a magnetic dipole with magnetic moment m2 moves in a non-homogeneous magnetic field in a 2D-Plane. This field is generated by another magnetic dipole with ...
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How do I derive a particular form of the Langevin equation from Mori's generalized master equation?

Preliminary: I have a generalized Langevin equation for a set of relevant operators, written in Liouiville space as $\{|A_{v}\rangle \}$, and obtained via Mori's projection operator technique: \begin{...
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Can there exist a motion which cannot be described as a function of time?

I know there exist systems for which we cannot solve its differential equation, But I was wondering if there could be a motion that cannot be represented as a differential equation with respect to ...
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Equality modulo equations of motion [closed]

What does Qmechanic mean by “equality modulo equations of motion” when talking about Lagrangian formulation/formalism and so on?
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Question of ball falling down.Difficulty in understanding the formula

A ball is thrown upward from the top of a tower 40m high. u = 10m/s.Find time for it reach AD. g = $10m/s^2$. Taking upwards direction as +ve and downward as -ve. u = +10m/s.$g=-10m/s^2$.s=-40. $-40 = ...
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"Equations of motions" and direction of maximal entropy

Say one has a system of statistical physics whose entropy is given as a function of one or multiple variables; for example as $S(x)$. An example of such a system could be a osmosis system, or a ...
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I want to know the difference in two methods I have solved [closed]

A thief is driving away on a straight road in jeep moving with a speed of 9 m/s. A police man chases him on a motorcycle moving at a speed of 10 m/s. If the instantaneous separation of the jeep from ...
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Can we determine the order of the equations of motion simply by looking at the action?

Naively, one would expect the EL equations arising from an action to contain derivatives (of the dynamics field) of an order that is twice the order of the highest-order derivative (of the dynamic ...
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Deriving conserved charges from the equations of motion

It is very well established how to derive conserved charges associated to the symmetries of Lagrangian using the Noether's theorem. Also in the Hamiltonian formulation, we know how to derive the ...
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Bullet piercing through block problem [closed]

A bullet moving with a velocity of 200cm/s penetrates a wooden block and comes to rest after traversing 4cm inside it . What velocity is needed for travelling distance of 9cm in same block. My though ...
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Lagrangian of a charged particle in a magnetic field (specific problem)

I have to determine the Lagrangian and the angular velocity $\omega = \dot\theta$, in cylindrical coordinates $(r, \theta, z)$, of a electron with mass $m$ and charge $-e$, wich is experiencing a ...
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Deriving the field operators for Quantum Field theories

I always see the form of the field operators derived by, in the case of a scalar spin 0 particle, imposing the field commutation relations on the classical field solutions of the Klein Gordon equation ...
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What is the difference between "field equations" and "equations of motion"?

I come across the terms "equations of motion" and "field equations" all the time, but what is the difference? For example, general relativity is described in terms of the Einstein ...
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Can we reverse the geodesic equation to find a metric for the theory?

The geodesic equation describes the motion of a particle moving in a straight line embedded in a curved geometry. $$\frac{d^2 x^\mu}{d\tau^2}+\Gamma^\mu_{\alpha\beta} \frac{dx^\alpha}{d\tau}\frac{dx^\...
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Stacked Block Problem [closed]

I am confused on a trivial problem here involving Newton's 3rd Law and the FBD of the following problem, where the question asks for the differential equation of motion, with $V_2$ as output and $...
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Motion of charged particle in uniform magnetic field and a radially symmetric electric field

This question posted by me on MSE talks about a physics problem. This is what it was: (I hope someone can help me with this) Consider a region of 2-dimensional space with a uniform magnetic field of ...
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Missing equations in Maxwells Equations

We have Maxwell's Equations (ignoring permittivity and permeability of free space) $$ \nabla\cdot E=\rho\;;\;\nabla\times E=-\frac{\partial B}{\partial t} $$ $$ \nabla\cdot B=0\;;\;\nabla\times B=\...
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Velocity of object on extremely low air density?

If we derive velocity in air when setting air resistance to $kv$, we'll get $$v= \frac{mg}{k}\left(1-e^{\frac{kt}{m}}\right) $$ and if air density goes to $0$, $k$ will also goes to $0$. When $t=T$ (...
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Equations of motion describing a great circle

I'd like to argue that equations of motions of the form $$\ddot \varphi = 0 \quad \text{and} \quad \ddot\theta = \sin\theta\cos\theta\dot\varphi^2$$ describe a great circle. I think the standard ...
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numerically integrating a trajectory in polar coordinates

So I've reduced my problem to not being sure how to integrate a trajectory in polar coordinates. Suppose I have a free particle and I express its Hamiltonian thus: $H =\eta_{ij}P^iP^j,$ where $\...
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Why can we use the equation of motion to calculate the amplitude in "Quantum Field Theory"?

I am reading the chapter on electron-proton scattering from "Quantum Field Theory in a Nutshell". The author calculates the amplitude of the electron-proton scattering (up to the second order). The ...
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In what sense are the equations of motion conserved by symmetries?

I am studying variational principles and I have been reading this set of notes by Townsend. In the first paragraph of Section 9, Townsend defines what it means for a transformation to be a symmetry of ...
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Rotation as an example of symmetry in classical mechanics

I modified the question because it was confused. On my book there is this mathematical definition of symmetry transformation: "The equations of motion have a symmetry, if the solutions of the ...
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Can we ignore the scalar field (dilaton) term in the Polyakov sigma-model action when deriving the classical equations of motion?

I have the full Polyakov sigma model action: \begin{equation} \begin{split} &S=S_P + S_B + S_\Phi = \\ &- {1 \over 4 \pi \alpha'} \Big[ \int_\Sigma d^2\sigma \sqrt{-g} g^{ab} \partial_a X^\mu ...
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13 votes
3 answers
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Why intuitively, do we define symmetries as transformations that map solutions of the equations of motion into other solutions?

Of course, strictly speaking, a symmetry is always a transformation that leaves a given object unchanged. But I'm curious why observable symmetries of physical systems are exactly those ...
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Does the equation of ball going up in gravity straight up with a vertical initial velocity hold when it's coming down?

Suppose a ball is thrown up and having the same altitude at different times. So should the equation of motion $ v_0t - gt^2$ which I derive from balancing forces hold for both the times when the ball ...
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Upward Moving Cable Car [closed]

A $1500$ kg cable car moves vertically by means of a cable that connects the ground and the top of the hill. What is the tension in the supporting (massless) cable when the cab, originally moving ...
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2 answers
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Can an Equation of Motion Do More?

My usual expectation is that an equation of motion should give me the time-evolution of a system given an initial condition. But I am curious as to can an equation of motion do more than that? In ...
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Are symmetries in the equation necessarily symmetries in the corresponding solution(s)?

I wonder whether the symmetries in the equations (such as the heat equation, the wave equation, the Schrödinger equation, Maxwell equations) are reflected into their solution(s). I.e., assuming that ...
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Equations of motion of a cylinder on a horizontal plane

How would I go about deriving the equations of motion for the motion of the centre of mass of the cylinder in this system: The cylinder has mass $M$ and radius $R$ and the small mass $m$ is being ...
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1 answer
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Transformation of generalized coordinates

One of the advantages of Lagrangian formulation is that the equations of motion have the same form regardless of the choice of generalized coordinates. Suppose that a system has $s$ degrees of freedom,...
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Do the equations of motion have specific characteristics?

I solved a classical mechanics problem in a form somewhat like this: $$x(t)=t^2+5t$$ $$y(t)=t^3$$ $$z(t)=5.$$ The problem asked me to find the equations of motion of an object. From my ...
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6 votes
2 answers
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Question about Type IIB supergravity equations of motion

This is probably a dumb question, but I'm a mathematician who's been trying to understand the equations of motion for Type IIB supergravity, and I'm not quite sure I understand what's going on with ...
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What does it mean to find an equation of motion, given vector functions that describe both the object's position and velocity?

I don't really understand how to approach a problem that asks to find the equation of motion. Intuitively, I would guess that an "equation of motion" is an equation where the particle's position is ...
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Showing the invariance of the equations of motion

It is strange to me that for a symmetry which involves $\dot{x}$, there seems to always appear a term with $\dddot{x}$ in the variation of the equations of motion, which doesn't makes much sense. I ...
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Is it valid to replace the equations of motion inside a symmetry?

For example, this symmetry: $$\delta q^{i}=\epsilon(q^{i}-2\dot{q}^{i}t)$$ it's derivative is: $$\delta\dot{q}^{i}=-\epsilon(\dot{q}^i +2\ddot{q}^i t)$$ There appears $\ddot{q}^{i}$ in this ...
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Is it strictly necessary to require gauge invariance of the action and equations of motion?

When writing down an action for a gauge theory, we require that the action be gauge invariant. This is typically taken to mean that the action must be written explicitly in terms of gauge invariant ...
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Physical significance of omitting a purely time dependent term from a Lagrangian

For a simple pendulum whose point of support moves on a vertical circle of radius $a$ with constant frequency $\gamma$, you can write the Lagrangian down. The potential energy can be written as $-mg(-...
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