Questions tagged [degrees-of-freedom]

This tag is for questions relating to the Degree of Freedom (DOF) of a mechanical system. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering.

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Degrees of freedom in a Kahlerian NLSM

Lagrangian for $d=1$ $\mathcal{N}=4$ SUSY model on a $n$-complex dimensional Kahlerian target space is given as (see p.213, eqn. (10.251) in the Mirror Symmetry book (pdf)) $$\begin{equation} L= ...
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Does the ideal gas law apply to gases which consist of more than one atom?

In the derivation of the ideal gas law, one sets for the average kinetical energy $f = 3$ degrees of freedom. This refers to the transition in x,y,z axes. This is true for gases, which consist of only ...
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Counting supersymmetries in $d=4$ vs in $d=1+1$

Having studied supersymmetry in $d=4$, my understanding is that we count supersymmetries by the number of pair of complex supercharges $$ Q_\alpha^I = \begin{pmatrix} Q_1^I \\ Q_2^I \end{pmatrix}~,~ \...
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7answers
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Why can't a particle rotate about its axis? [duplicate]

When treating an atom as a point partcle, it is usually assumed that it cannot rotate about its axis. Is it that anything considered as a point particle cannot rotate about its own axis? If so, why is ...
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What is 'degrees of freedom' when using Fourier series to express a periodic waveform?

We can express any desired periodic waveform using Fourier series. In the book I am studying from it's said: 'We see that with Fourier series, we can produce any desired periodic waveform and extract ...
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Degrees of freedom for a bead on a parabolic wire?

How many degrees of freedom does a bead on a parabolic wire have? I think it must be two degrees of freedom since the bead is constrained to move on the wire (up, down motion and left/right motion). ...
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How do you find the degrees of freedom of a rigid body moving parallel to a fixed plane surface? [closed]

Find the degrees of freedom of a rigid body moving parallel to a fixed plane surface. I know the definition of degrees of freedom which meant we need minimum number of coordinate to specify something....
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A problem on Degrees of Freedom

Degrees of freedom of a massless rod, moving freely in space with a speck which is constrained to move on it? It seems massless rod is ideal I am very confused how to regulate degrees of freedom. ...
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1answer
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Does emergence or the second law create more degrees of freedom total? [closed]

Here's my layman thought process: By emergence and the second law, new "modes" or points in configuration space become "unlocked" with macroscopic systems. One is a brain, which ...
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1answer
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How to count degrees of freedom in a symmetric $N \times N$ matrix?

I am reading Wayne Hu's short lecture on cosmology mathematical infrastructure (https://arxiv.org/abs/astro-ph/0402060), and have several questions. Some background for us lazy people that don't want ...
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Why particles can have different number of degree of freedom in a 3D + 1T dimension?

Air molecule has $6$ degrees of freedoms: it can move up & down, left & right, front & back, rotate along $x$-axis, $y$-axis, $z$-axis. But I heard about graviton, a hypothetical particle ...
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Gauge transformation vs field excitation

I think I'm fundamentally misunderstanding something. Say I have a gauged Lagrangian for a complex scalar field $\phi$ with no SSB: $$\begin{equation} \mathcal{L} = (D_{\mu}\phi)(D^{\mu}\phi)^{\dagger}...
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Factor $f$ of internal energy of a gas

For a $n$-atomic gas in any sort of geometry, The formula for $f$ is $$f = 3n- \text{number of constraints}.$$ The way I was taught this formula was like each $n$ particles< there is $3$ ways it ...
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The degree of freedom in kinetic gas theory

What is the degree of freedom in kinetic gas theory? How can I determine how much degree of freedom some molecule has?
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Has really general relativity only two degrees of freedom (as in the Maxwell theory)? [duplicate]

i read in a "a first course on loop quantum gravity" written by Gambini that: "General relativity is invariant under spatial coordinate transformations. The constraint associated with ...
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Is the number of spin states necessary in the density of states function?

I'm studying how to calculate the density of states in the final configuration in order to apply Fermi golden rule. For free EM field the following expression is the starting point: $$d^3n=\frac V {(2\...
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How do we know from representation theory that a massless spin-1 particle has only two polarizations?

In chapter 8.2.3 of Schwartz' textbook "Quantum Field Theory and the Standard Model", the author states the following, Finally, we expect from representation theory that there should only be two ...
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Generalized coordinates of two unequal masses attached to a mass-less rigid rod

Consider a system of two particles of masses $m_1$ and $m_2$ moving in a plane. Let the respective position vectors be $\mathbf{r_1}$ and $\mathbf{r_2}$. The particles are attached at the end of a ...
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Is three dimensional supergravity dynamical?

So it is well known that standard $D = 3$ Einstein gravity is non-dynamical in the sense that the graviton has no on-shell degrees of freedom (d.o.f $= D(D-3)/2$ and the theory is topological). ...
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Gauge invariance and the degrees of freedom [duplicate]

I am currently starting to learn some QFT. And I am very confused by the fact that the freedom to choose a gauge for a theory controls the physical degrees of freedom. Please correct me if i am wrong ...
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What is the origin of the irreducible error $\propto e^{-N}$?

In this (timestamped) lecture, the professor says that any measurement includes an irreducible error that scales as $e^{-N}$ where $N$ is the number of degrees of freedom in the measurement apparatus ...
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Effective degrees of freedom of relativistic gases: Intuition for fermion factor 7/8?

When calculating the number density of a gas of identical massless particles you get the following integral $$ I_{n,\,\pm} \equiv \int_0^{\infty} \frac{u^2}{e^u\pm1} \,\text{d}u $$ with (+) for ...
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Reviewing an old argument about the number of DOFs of EM field

For free electromagnetic fields, it is possible to choose a gauge such that the scalar potential $\phi(t,{\bf x})=0$ and the vector potential ${\bf A}(t,{\bf x})$ satisfies the Coulomb gauge condition ...
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How do I calculate the bosonic/fermionic degrees of freedom from the helicity content?

After constructing a physical state and discovering the particle content, how can one find the fermionic and bosonic degrees of freedom? Eg. Constructing the physical states of an $\mathcal{N} = 2$ ...
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How do Maxwell's equations uniquely determine ${\bf E}$ and ${\bf B}$ despite no. of equations exceeding no. of unknowns?

Maxwell's equations in free space are given by $${\bf\nabla}\cdot\textbf{E}=0,~~{\bf\nabla}\cdot\textbf{B}=0$$ and $${\bf\nabla}\times\textbf{E}=-\frac{\partial\textbf{B}}{\partial t},~~{\bf\nabla}\...
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Lagrangian Mechanics - Bead sliding on a rotating rod

Say i have a bead of mass $m$ sliding on a friction-less rode (or wire) that is rotating with a permanent angular velocity $ω$. The whole system is under the influence of a uniform gravitational field ...
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Theory on domain walls

In Baryons in Quantum Chromodynamics, Zohar Komargodski have slide: I wanna understand: Why domein wall can have nontrivial worldvolume theory? When such solitonic objects have interior degrees of ...
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How many degrees of freedom does the air have?

Very simple question that I am overthinking... But how many degrees of freedom does the air have? Assuming let's say the air is confined in a rigid box.
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Regarding number of degrees of freedom of a dynamical system (as well as it's relation to number of equations of motion)

I would like to know why in the context of vibrating systems, we define degrees of freedom in terms of number of independent coordinates (by coordinates I mean the numbers which specify the components ...
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Does no-level-crossing theorem (aka avoided crossing) always hold in perturbation theory?

In perturbation, J.J. Sakurai Modern Quantum Mechanics Second Edition page 310 stated a no-level-crossing theorem stated that "a pair of energy levels connected by perturbation do not cross as ...
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1answer
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About Degrees of Freedom and Energy

We know that the degree of freedom of oxygen is 5. For this the total kinetic energy of oxygen must be (5/2)nRT. But maximum books say that it should be (3/2) nRT where as our college teacher said it ...
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Degrees of freedom of constrained rigid body

A rigid body constrained at a distance $r$ from its center of mass with a ball-and-socket type constraint is considered to only have three (rotational) degrees of freedom. But isn't rigid body's ...
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1answer
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Question about gauge symmetry confronted in Schwartz‘s book

This picture is from Schwartz book on QFT on page 131. I cannot understand that: What does the orange underlined sentences mean? How is Equation 8.108 derived? Could anyone kindly make some further ...
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According to equipartition theorem, how a harmonic oscillator has two degree of freedom?

I was reading a book on kinetic theory. In the part of equipartition theorem, I found a line as follows, " The average energy corresponding to one vibration is equal to twice the K.E. corresponding to ...
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Why a molecule has $3N$ degrees of freedom?

An atom has $3$ degrees of freedom because it can possess energy in $3$ independent ways- Kinetic Energy in three independent directions. Therefore, a collection of $N$ atoms will have $3N$ degrees of ...
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Difference between finite and infinitesimal motion

I am studying Arnold Sommerfeld mechanics. Here they talk about finite and infinitesimal motion. Quoted from the text: The simplest example of a non-holonomic condition is furnished by a sharp ...
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2answers
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Do physical fields always have dimension of the Tangent Space at a point?

Say we only consider classical fields in 3 dimensions. In a 3 dimensional space you have scalar or vector fields, where scalar fields can be understood as vectors of one dimension. The other physical ...
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Validity of equipartition theorem and choice of coordinate axis

While reading through the basic derivation of how kinetic energy is related to temperature, I stumbled upon equipartition theorem where $\frac{1}{2}mv^2 = \frac{1}{2}kT$ thus $\frac{3}{2}kT$ in 3-...
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Wilsonion Renormalization Group in Asymptotically Free Theories

Consider some correlation function computed at some renormalization scale $\mu_0$ in an asymptotically free theory $$ \langle M(z; \mu_o) \rangle. $$ From what I understand of renormalization-group ...
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Degree of freedom of diatomic molecule [duplicate]

Is there any justification for degree of freedom of diatomic molecules to be two? I believe that degree of freedom are the number of coordinates needed to specify the position of a molecule so how ...
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What are degrees of freedom in this context?

For translational motion, $$H_\text{trans} = \frac{p_x^2}{2m} + \frac{p_y^2}{2m} + \frac{p_z^2}{2m}$$ For rotational motion, $$H_\text{rot} = \frac{1}{2} \frac{L_x^2}{I_x} + \frac{1}{2} \frac{...
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Degrees of freedom of large molecules

I know how to calculate degrees of freedom for small molecules, but how do I calculate degrees of freedom for larger molecules? For example, Benzene.
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graph relativistic degrees of freedom

I'm trying to graph the relativistic degrees of freedom, which should look like the figure And I am trying to guide me with this Phys.SE answer: Number $g(T)$ of relativistic degrees of freedom as a ...
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1answer
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Number of independent components of the electromagnetic field

I'm taking a course on electrodynamics and I'm confused when we start talking about potentials. The electromagnetic field seems to have 6 independent components to me. It's described by six dynamical ...
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1answer
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Spin of the particle and degrees of freedom

Wigner showed that irreducible representations of the Poincare group can be listed, depending of the mass being zero or larger then zero, as $2J+1$ dimensional representations where $J$ is half-...
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How many degrees of freedom does a system have if we only eliminate some of the constraints?

At the very bottom of page 11 in his The Variational Principles of Mechanics, Lanczos says the following: We sometimes prefer to eliminate only some of the kinematical conditions, and to leave the ...
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How constraining are conservation laws and continuity principles?

Suppose there are $N$ particles with masses $m_1, m_2, ..., m_n$. Consider the $3N$-dimensional classical configuration space of such particles. Consider some arbitrary physically possible trajectory $...
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Degrees of freedom of a molecule

We all know that if we consider a mono-atomic molecule, it has $3$ translational degrees of freedom only, along the $3$ principal coordinates of the Cartesian coordinate system. In case of a ...
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1answer
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How to count degrees of freedom of metric in Newmann-Penrose formalism?

Usually a metric has 10 degrees of freedom. How to show the same in Newmann-Penrose formalism?
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Why do the degrees of freedom of a density operator not match up with the degrees of freedom of a state vector? [duplicate]

The density operator $\rho$ of a mixed 2-qubit system has $4^2-1=15$ degrees of freedom. We can require Tr[$\rho^2$] $ =1$ so that the system is in a pure state. Now we have 14 degrees of freedom. If ...

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