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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Degree of freedom - Lorentz transfomation reduces it? [duplicate]

I am having a real difficult to counting degree of freedom. In fact, I notice that sometimes I am confused about what exactly we count as DoF, and what we do not count. See, for example, the ...
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Counting degrees of freedom in theories with two-forms [duplicate]

I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
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Is Bohr's model one-dimensional?

Purdue university in its article on Bohr's Model explains: At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular ...
Govind Prajapat's user avatar
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Is the number of degrees of freedom always equals one?

If the number of degrees of freedom is the minimum number of independent variables necessary to describe the system, does this mean that this number is always equal to one? For example, if, as it ...
Mikhail's user avatar
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Equal average energies in translational and rotational degrees of freedom

In, An Introduction to Thermal Physics, Schroeder states It’s not obvious why a rotational degree of freedom should have exactly the same average energy as a translational degree of freedom. However, ...
GedankenExperimentalist's user avatar
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How many degrees of freedom does a diatomic and triatomic molecule have at high temperatures?

I understand that a diatomic molecule has 3 translational and 2 rotational degrees of freedom. But since there is only 1 vibrational mode associated with a diatomic molecule and 1 vibrational mode is ...
Srijan Das's user avatar
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Is the equation for degrees of freedom $f=3N-k$ valid for all cases?

Consider the example of a linear triatomic molecule. Now at low temperatures, where we can exclude vibration, quite clearly degrees of freedom, $f=5$, with 3 translational and 2 rotational degrees of ...
Srijan Das's user avatar
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How many independent equations do Maxwell's equations represent in arbitrary dimensions?

In an arbitrary number of spacetime dimensions $D$, Maxwell's equations are \begin{align*} \mathrm{d}F &= 0, \\ \mathrm{d}(\star F) &= -J. \end{align*} How many independent equations does this ...
tparker's user avatar
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Degrees of freedom in a molecule of $N$ atoms

I am trying to understand why the number of degrees of freedom in a molecule, $3N$, is the same as the number of degrees of freedom of $N$ independent particles. Why do the molecular constraints like ...
Emerson's user avatar
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Regarding Degrees of Freedom and dynamics of polyatomic molecules [closed]

Justify how a molecule with N atoms have $3N-5$ vibrational degrees of freedom(Linear) and $3N-6$ vibrational degrees of freedom (Non-linear). Will this be valid for large number of N? Taking $H_2O$ ...
Aditya Krishna Panickar's user avatar
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Doubt regarding kinetic theory of gases

My school teacher had told me that one of the assumptions of Kinetic Theory of Gases was that the molecules of a given gas were all identical and to be considered as very small elastic spheres. ...
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Difference between Kopp-Neumann and Dulong-Petit law?

So this is basically a follow-up to this question: How many degrees of freedom does the water molecule have? I've done some further research and found that the main difference between Dulong-Petit and ...
Zedssad's user avatar
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Why expansion of real gases lead to cooling?

Paul Hewitt writes in his book Expansion of real gases lead to cooling as average translational kinetic energy per molecule decreases. The reason given is: During Expansion molecules collide with ...
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How many degrees of freedom does the water molecule have? [duplicate]

This is mainly a question about molar heat capacity. I've read many different values for the degrees of freedom of water, for example f = 12 on (https://en.wikipedia.org/wiki/Molar_heat_capacity). But ...
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Why the massive spin-1 photon gets more degrees of freedom than massless case; while the massive spin-1/2 electron stays the same as massless case?

Spin 1 field without mass term like photon has 2 real degrees of freedom. The polarization with two states. I think I can denote it as quantum state $|s,s_z> = |1,1>$ and $|1,-1>$. Spin 1 ...
zeta's user avatar
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Fermionic and bosonic degrees of freedom of a vector superfield

I am currently studying supersymmetry with the SUSY primer of Stephen P. Martin (https://arxiv.org/abs/hep-ph/9709356) and there seem to be not equally many bosonic and fermionic degrees of freedom (...
FlavonBSM's user avatar
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Why does a degree of freedom vanish from 3D to 2D in that tensor construction?

Let's assume an arbitrary tensor in 3D coordinates: $g_{ij} $ with $i, j$ in $[1,3]$. It shall be arbitrary, meaning not symmetric. It has 9 entries which equals 9 degrees of freedom (dof). Now, I ...
MartyMcFly's user avatar
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1 answer
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The equipartion theorem and degree of freedom in case of vibration

I have been taught in chemistry that, the energy of a vibrational freedom is $RT$ (ie, twice that of rotational/translational) The degree of freedom which I found in chemistry, for the vibrational ...
Ninjametry's user avatar
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2 answers
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How can an object have more than 3 degrees of freedom?

In 1 of my robotics classes our professor told us that something can have up to 6 degrees of freedom:translation in the x axis , translation in the y axis,translation in the z axis,rotation around the ...
Cerise's user avatar
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On counting the DOF of EM wave polarization

I've got a few questions: In a direvation I've seen, it's 4->3->2: in Lorenz gauge, by solving d'Alembert equation we get $A^\mu=\mathcal{A}\varepsilon^\mu e^{i(kz-\omega t)}$, and $\varepsilon^...
coder114514's user avatar
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Tensor/Vector decomposition/representation & DOF argument

In fluid mechanics, for irrotational flow it is sometimes useful to present the velocity, $U$ in terms of a scalar potential $\Phi$ as: $$\vec{U}=\nabla \phi$$ $\vec{U}$ has 3 dof. $\phi$ has 1. Why ...
sis's user avatar
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How many relativistically invariant degrees of freedom in $n$-particle scattering?

Suppose we have a scattering process with $n$ external legs with four-momenta $p_1, \cdots, p_n$. Naively there are $4n$ degrees of freedom, however most of these putative degrees of freedom are not ...
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Spin 3/2 field in higher dimensions

The Lagrangian and equation of spin 3/2 field in a general dimension D is given on page 96 of Supergravity ( textbook by Freedman and Proeyen, 2012 ). The action is : $$ S = - \int d^Dx \bar{\psi}_{\...
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Counting States for $N$ SUSY in Wess and Bagger [closed]

In Wess and Bagger's book, we calculate how many states are there for massive cases under $N$ SUSY. We couldn't follow the table on page 14. What is "Spin" here (absolute value?), and how ...
Nek's user avatar
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Degrees of freedom in the early universe with MSSM?

As nicely summarized on P4 in On effective degrees of freedom in the early universe here; at high temperatures where all the particles of the Standard Model are present, we have 28 bosonic and 90 ...
Mr Anderson's user avatar
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How many dimensions are in the electromagnetic field?

This question asks how many dimensions there are in the electric field for the purposes of better understanding polarization. However, the other answers don't seem to fully address the question, and ...
Sven Voigt's user avatar
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How many degrees of freedom does a photon have in 2+1D?

Wigner's classification of particles implies that the internal degrees of freedom of a particle transform under unitary representations of the subgroup of the Lorentz group that leaves its momentum ...
Panopticon's user avatar
2 votes
1 answer
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Frenkel or Tulczyjew-Dixon Condition and QED

What is the physical motivation behind imposing Frenkel's condition, $$p_{\mu}S^{\mu\nu}=0$$ for an electron of momentum $p$ and spin given by some tensor $S^{\mu\nu}$? In addition, a direct ...
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How many independent degrees of freedom does the metric tensor have in vacuum (at every point)?

A field of metric tensors fully characterises the curvature of a vacuum space-time. (For example, the spacetime between some single point masses which are themself not part of the manifold) The metric ...
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Is there a general argument for why non-dynamical degrees of freedom show up in the propagation of massless gauge bosons?

In both spin-1 and spin-2 gauge theories, the gauge bosons (e.g. the photon & gluon and the graviton respectively) have two physical degrees of freedom, which can be observed quantum mechanically ...
Panopticon's user avatar
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1 answer
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Deriving the gauge group from the little group

Arguments from the "little group" are used to show that the internal degrees of freedom of a massive particle transform under $SO(3)$, while the internal degrees of freedom of massless ...
Panopticon's user avatar
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How did the number of unknowns change in the Dirac equation?

So I haven't seen this argument addressed in any textbook which makes me doubt it's legitimacy. Here goes: Since Newton's $F=ma$ is essentially a second-order differential equation. Any equation of ...
More Anonymous's user avatar
4 votes
1 answer
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Counting number of equations for Rarita-Schwinger field (in Supergravity textbook)

I am reading the book "Supergravity" by Freedman and van Proeyen (2012). On page 96, they are talking about the equation of motion of massless vector-spinor field (the spinor index is ...
baba26's user avatar
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1 answer
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Degrees of freedom in Gaussian Normal Coordinates in GR

I'm learning about GR and have been wondering about something. At any point, we can define Gaussian Normal Coordinates which are orthonormal and approximately flat (first derivative along all axes is ...
Timothy O'Brien's user avatar
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Degree of freedom and Grubler formula

I am attempting to apply the Grubler formula (which can be found here: https://learnmech.com/how-to-calculate-degree-of-freedom-of/) to determine the number of degree of freedom, but it does not seem ...
c.leblanc's user avatar
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Number of degrees of freedom for a gaseous mixture

I came across the formula to find the number of degrees of freedom in a gaseous mixture which is as follows: $$f_\mathrm{mix} =\frac{\sum n_if_i}{\sum n_i}$$ Now it has been mentioned in this lecture ...
reverseambition's user avatar
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2 answers
153 views

What is the independent variable in electromagnetism?

As we know, In a circuit, simple or complex, electric fields created by surface charges move electrons which creates current which creates magnetic field which can be coupled to other lines and induce ...
dsplover123's user avatar
5 votes
3 answers
772 views

Doubt in Arnold's "Mathematical Methods of Classical Mechanics", Chapter 2

My question is about Arnold's book "Mathematical Methods of Classical Mechanics", chapter 2, section B (pg. 16). He talks about systems with one degree of freedom, i.e. systems described by $...
algebroo's user avatar
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Does off-shell graviton in 3+1D still have two degree of freedom?

In general relativity, on-shell spin 2 graviton has 2 degree of freedom in 3+1D due to gauge symmetry, which is because of einstein equation, however, for off-shell graviton, does it still have 2 ...
feng lin's user avatar
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Why is the heat capacity of water $9R$ and not $6R$?

From the equipartition theorem, the relationship between energy and temperature in a substance is $U=\frac{NRT}{2}$ for $N$ quadratic degrees of freedom associated with a particle of that substance. ...
cbushofsky's user avatar
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Residual gauge freedom and complete residual gauge fixing in lorenz gauge

What I understand after reading all answers from physics stack exchange related to residual gauge freedom and complete residual gauge fixing are as follows; The gauge transformation is: $A'_{\mu}$=$A_{...
Keshav shrestha's user avatar
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What are non-propagating fields?

I have read at different places that in 3 spacetime dimensions, there are NO propagating gravitational degrees of freedom. This seems to imply that we have only "non-propagating" degrees of ...
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$R_\xi$ gauge and degrees of freedom counting

In the standard classical Maxwell theory, we use the following arguments to claim that there are only two propagating degrees of freedom $A_\mu$ has 4 components $A_0$ is non-dynamical (-1) $\...
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Elastic collisions and internal degrees of freedom

As I was considering elastic collisions today a question popped into my head. Do elastic collisions imply that there are no internal degrees of freedom in the colliding objects which couple ...
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How many independent equations are contained in $R_{rsmn}=0$ in consideration of the Bianchi identity?

In $d$ dimensions, how many independent equations are contained in $R_{rsmn}=0$ in consideration of the Bianchi identity $\nabla_{[a}R_{bc]de}=0$? This discussion reveals the independent equations ...
John Doe's user avatar
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1 answer
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Why do systems of $n$ coupled oscillators have $n$ normal modes?

Consider a linear system of $n$ differential equations with constant coefficients corresponding to a physical scenario where I have $n$ coupled oscillators (like $n$ masses attached by springs in ...
Mason Giacchetti's user avatar
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2 answers
281 views

How does a field $\phi(x,t)$ have infinite degrees of freedom and why are its inputs labels not variables?

Consider a classical Lagrangian $L(q, \dot{q})$, which by definition has a discrete number of degrees of freedom. Now suppose we have a quantum field (or any field) which we denote by $\phi(x,t)$. It ...
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How to Conceptually Understand Long Wavelength Fluctuations?

I have been trying to conceptually understand long-wavelength fluctuations of degrees of freedom, and I have been reading this (RG) to do so. I understand was it means for a degree of freedom to ...
user333905's user avatar
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What do we mean by "Degrees of Freedom" when we Talk about the electromagentic field?

For point-like particles, the term "degree of freedom" seems rather clear: It's the number of independent coordinate functions $q_i(t)$ that we need to specify to completely describe the ...
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Degrees of Freedom in the Newman-Penrose Formalism

In the Newman-Penrose formalism one encodes the ten degrees of freedom of the Weyl tensor $C_{\alpha\beta\mu\nu}$ in the five complex scalar potentials $\Psi_0$, $\Psi_1$, $\Psi_2$, $\Psi_3$ and $\...
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