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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Physical parameters for spin 1/2 particles

I am having trouble to understand what it means by "physically relevant real parameters" and how does it help us to specify a quantum system. Let say, we have a state of k half spin ...
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All possible choices for two independent intensive variables for a one-component, one-phase system

I am confused about the independent variables in thermodynamics. I know that for a one-component, one-phase system, there are only two independent intensive variables that can be chosen and which ...
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Double Spring Damper Mass System Transfer function

I am attempting to find the resonance frequency of a double mass spring system as shown in the image. I need to find the resonance frequency so that I can input it into my sin wave generator in MATLAB ...
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Rotational equation for variable mass in Simulink/Matlab ignores relative angular velocity of the mass flow?

I am doing a simulation using Simulink/MATLAB. The block I am using called "Custom Variable Mass 6DOF (Euler Angles)". Here is the documentation of this block: https://www.mathworks.com/help/...
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Completeness of Maxwell's equations

If we consider Maxwell's equations in the form: $\nabla\cdot\overrightarrow{E}=\frac{\rho}{\epsilon_0}$$\nabla\cdot\overrightarrow{B}=0$$\nabla\times\overrightarrow{E}=-\frac{\partial\overrightarrow{B}...
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Are gravitons possible in 2+1 spacetime dimensions?

Spin-1 massless particles are transverse waves, so they need at least three space-time dimensions to exists. As for gravitons, I think they are still not possible in three dimensions, and to reveal ...
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1answer
28 views

Properly accounting for indistinguishability of (homonuclear) diatomic molecules in “internal” partition function

I have always liked Schroeder's take on the partition function being a product of translational and internal degrees of freedom: $$ Z_1 = Z_{\text {trans}} Z_{\text{int}} $$ where $Z_{\text{int}}$ can ...
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73 views

Why isn't energy conservation equation sufficient to determine the motion?

The star of large mass $M$ is orbited by planets of masses $m_1$ and $m_2$. The energy conservation equation for this system is$$\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}-MG\left(\frac{m_1}{...
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Confusion with degrees of freedom [closed]

I am facing a lot of confusion regarding the degrees of freedom of various molecules. I want to know some facts with certainty. I will talk about what I have read, please correct me if I am wrong. I ...
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183 views

Understanding dependent/independent variables in physics

How does one determine the independent and dependent variables? What do the terms mean? Can they be derived from a formula? For example I saw in a textbook $F = k\Delta l$, Hooke's Law, that $F$ is ...
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117 views

Number degrees of freedom for Sphere on a inclined plane

How many generalized coordinates are required to describe the dynamics of a solid sphere is rolling without slipping on an inclined plane? What I think is that there two translational degrees of ...
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How does gauge symmetry constrain the dynamics of a field's physical degrees of freedom?

My rough understanding of gauge theory is that some of a field's degrees of freedom (d.o.f.) may turn out to be "non-physical" due to local symmetries. But does gauge symmetry constrain the ...
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What is the theoretical justification for the Law of Equipartition of Energy?

What is the theoretical justification for the Law of Equipartition of Energy? Why are equal energies distributed in each degree of freedom even though sometimes they are completely different (like ...
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179 views

How many Degrees of Freedom do Linear Triatomic Gas Molecules Have and Why?

I read this in one of my textbooks that stated Linear Triatomic Gas Molecules like CO2, HCN, CS2 in which all the atoms are linear, the total number of degrees of freedom are Nf = NT + NR + NV where ...
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1answer
50 views

What are the physical degrees of freedom in Yang-Mills theories?

I am pretty familiar with the Lagrangian formulation of quantum electrodynamics and perturbation theory techniques; however, I am hoping to move into QCD and other Yang-Mills Theories. As I do, I am ...
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42 views

Number of degrees of freedom if independent coordinates are functions of time

If there are $n$ independent coordinates for a system of particles, but all of them are functions of time, is it correct to say that the degree of freedom is 1? If we know the instant of time we're ...
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81 views

Degrees of freedom of a rolling sphere [closed]

How many degrees of freedom does a sphere rolling on a smooth (frictionless) plane has?
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6answers
173 views

Degree of freedom of a Sphere

We all have learnt that a single atom posses 3 translational degree of freedom and no other. But it happen to be a sphere too. Is it correct to say that a sphere has 3 rotational degree of freedom? ...
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70 views

How to make derivative of antisymmetric tensor?

When I read the Conformal Field Theory of Di Francesco et al, I found I will get two different answers from the same expression. To get the (2.131) $$ \dfrac{\delta x^{\mu}}{\delta\omega_{\rho\nu}}=\...
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28 views

How to determine the degrees of freedom and generalised coordinates in this satellite exercise?

(image below) We have a satellite on an elliptical orbit. m1=m2=m in this case. The problem is only 2 dimensional in the x-y-plane. One should determine the degrees of freedom and choose suitable ...
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1answer
65 views

Understanding vibrational mode of a molecule and its contribution to average energy

I'm facing difficulty understanding how vibrational energy modes contribute to a molecule's average energy (or heat capacity). What I know is : For a polyatomic non-linear molecule, there are $3N-6$ ...
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139 views

How to determine the number of generalized coordinates in the following example?

Question: In this exercise one needs to determine the generalised coordinates. We have a pendulum in a magnetic field $B$. The pendulum rotates around its axis with an angular velocity $ω$ on the ...
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How to determine the number of constraints in this problem set?

I don't understand how to determine the number of constraints in this given problem set in classical mechanics (picture attached down below). Now lets take a look at this problem for example where a ...
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What is the internal energy of water vapor? OR How many degrees of freedom does $\rm H_2O$ have?

Here are the "knowns" that I'm working with. Internal Energy for a monatomic gas is $$U = (3/2)nRT$$ For a diatomic gas its $$U = (5/2)nRT$$ All of my textbooks and online sources indicate ...
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66 views

How many degrees of freedom are there in the universal physical constants?

If you were to change one universal physical constant (say, electron charge) then the universe would behave differently in observable ways. For one thing, this would change the fine structure constant,...
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Why do some gases have fewer degrees of freedom at same temperature?

I am trying to understand the degres of freedom for gases. Air has 5 degrees of freedom at room temperature but why does Argon, $Ar$ have 3 degrees of freedom while $O_2$ has 5 at the same temperature ...
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77 views

What does this graph represent?

I dont understand the second graph below. If I understand the first one right, it represents the potential energy between two atoms. So if we bring them closer together or separate them past the ...
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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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1answer
49 views

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
206 views

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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80 views

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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1answer
83 views

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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1answer
168 views

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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2answers
126 views

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
38 views

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
156 views

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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1answer
40 views

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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74 views

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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3answers
66 views

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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43 views

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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36 views

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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32 views

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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1answer
258 views

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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67 views

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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55 views

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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56 views

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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60 views

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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62 views

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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