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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Number of Degrees of Freedom of a Rigid Body System - Proof

Let us define the number of degrees of freedom of a material system as the number of scalar parameters needed to know the position of each particle of the system with respect to any inertial frame of ...
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What is a propagating degree of freedom?

Given a gauge field theory, the various fields involved have (pointwise) degrees of freedom. For instance, if I consider the gauge theory of gravity in four dimensions, I have a set of tetrads $\{ e_\...
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How many constants of motion are there in a 2D two body problem?

A system consists of two masses interacting with gravitational force, rotating around their centre of mass. If we only consider the $xy$ plane where the masses rotate, the system has 8 degrees of ...
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The effect of the non-existense of longitudinal polarisation mode of the photon on equipartition theorem

Massless vector bosons like photons only have 2 independent polarisation degrees, unlike massive vector bosons. For a spin 1 boson with mass $\mu$ and with $k^λ = (ω, 0, 0, k)$ the longitudinal mode ...
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Degrees of freedom for Constrained Motion

I'm starting to learn about Degrees of freedom, and the idea of 'constrained motion' seems strange to me, surely any particle with a predefined path is 'constrained' in its motion, We also had ...
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How much degree of freedom of a rigid body in $N$-dimensional space?

Well I have the answer it is $\frac{N(N+1)}{2}$ but what the procedure to derive it . I tried this. 1).I have $N$ number of translation freedom. To calculate the number of rotational freedom I tried ...
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How many independent equations are contained in the Bianchi identity?

In consideration of the various symmetries of the Riemann curvature tensor, how many independent equations are contained in the Bianchi identity $R_{rsmn|t}+R_{rsnt|m}+R_{rstm|n}=0$ ? Symmetries of ...
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How many field components are there in vector-spinor field?

I am trying to find out the degrees of freedom of the vector-spinor field ($s=3/2$). The degrees of freedom are given by $N=\frac{1}{2}\left(N_{F}-N_{C}\right)$ for this spin where $N_F$ is the number ...
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Why does the Lorenz gauge $\partial_\mu A^\mu=0$ eliminate the spin-0 part of $A^\mu$?

Schwartz' QFT textbook states on page 116 that: Since $\partial_\mu A^\mu=0$ is a Lorentz-invariant condition, it has to remove a complete representation, which with one degree of freedom can only be ...
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Why are $p$ and $q$ independent variables in Hamiltonian formalism?

Let's say we have $(q, \dot{q})$ as the generalised coordinate and generalised velocity. If we have a Lagrangian given by $$L=Aq\dot{q}+Bq$$ where $A$ and $B$ are constants that give the right units ...
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Why should degrees of freedom be independent?

To define the position of a system of $N$ particles in space, it is necessary to specify $N$ radius vectors, i.e. $3N$ co-ordinates. The number of independent quantities which must be specified in ...
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Is $n=1$ (degrees of freedom) for monatomic?

In $PV=nRT$, $n$ is degrees of freedom. While in $PV=Nk_BT$, N is number of moles in a molecule. So value of $n$ is $3$, $5$ and $6$ for monatomic, diatomic and polyatomic respectively. But in the ...
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Why there are so many spinor components in higher dimensions if the number of degrees of freedom is only 2?

In the book of Freedman & van Proeyen on Supergravity a table (3.2) can be found which shows for dimensions from 2-11 the number of components of Majorana spinors. For instance in 4 dimensions we ...
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How many real degrees of freedom do Euclidean spinors have in 3D Euclidean space?

For the Euclidean case, we have that spinors transform under the $\mathbf{2}$ representation of (the double cover of) $SO(3,\mathbb{R})$. It would seem to me that since vectors live in $\mathbf{3}$, ...
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Why is there a $1/2$ in the definition of energy per degree of freedom $E=(1/2)kT$?

I was looking for an authoritative definition of Boltzmann's Constant. That led me to this discussion on NIST's site: Kelvin: Thermodynamic Temperature Thus, internal energy and temperature are ...
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Average kinetic energy vs Average energy

Actually, there is a similar question, but no answer for it. Statistical mechanics - average particle energy, average kinetic energy Here is the question: A. From Boltzmann distribution we can have ...
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Do angular equivalents of linear equations in physics reveal extra information?

First of all, This question is completely based on intuition and some concepts of mathematics. I have been thinking about this now for 5 months and haven't figured it out yet. I am beginner in physics ...
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"One-parameter" gauge transformation

In my advanced classical physics course, it was stated that the electromagnetic field strength tensor $F_{\mu\nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu}$ is invariant under "one-...
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The role of the Weyl-tensor in gravitation

In his book "Road to Reality" section 19.7 Roger Penrose asks the question: What is the appropiate analogue of the Maxwell field tensor $F_{ab}$ describing the gravitational degrees of ...
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What is the relationship between degree of freedom?

We know that $p=\dfrac{1}{3}\dfrac{M}{V}<c^2>$ Where p is pressure M is mass V is volume c is speed Noted that for monoatomic gas ,the energy is $\dfrac{3}{2}kT$,while for diatomic gas ,it is ...
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Do physical systems have intrinsic degrees of freedom that are independent of its representation?

Considering just the Newtonian case, suppose we have a system described by $n$ canonical position-momentum pairs, $(p_1,q_1),\dots,(p_n,q_n)$, and a Hamiltonian $H$. If we "scrubbed" all the ...
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What causes the degrees of freedom to be halved for Majorana fermions?

In many textbooks and on this site (nanophys answer here) it is stated that 'Majorana Spinors have half the degrees of freedom of a typical Dirac spinor'. A generic spinor in 3+1D has 8 degrees of ...
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What is the Laplace transform of a Linear Time-Varying system?

The Problem I have the following damped mass-spring system in the form of a Linear Time-Varying (LTV) system: $$\mathbf{M}(t)\mathbf{\ddot{x}}(t) + \mathbf{C\dot{x}}(t) + \mathbf{Kx}(t) = \mathbf{f}(t)...
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How to find the steady state response of a Multi-Degree of Freedom (MDOF) system?

The Problem I currently have a Multi-Degree of Freedom (MDOF) system with the following equation: $$\mathbf{M\ddot{X}}+ \mathbf{D}(t)\mathbf{\dot{X}}^2 + \mathbf{C\dot{X}} + \mathbf{KX} = \mathbf{F}(t)...
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Representation of Holonomic Constraints by independent generalized coordinates

Say we have a system with N particles described by N position vectors: $\{\vec{r_{i}}\};$ $i=1,...N$ Say we have a holonomic constraint: $$f(\{\vec{r_{i}}\},t)=0 \tag{1}$$ Since we have one holonomic ...
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Entropy - can we express number of microstates as a function parameterized by degrees of freedom?

In some of the answers and comments from this question people contended (not in so many words) that because entropy is parameterized by number of microstates $\Omega$, and the definition of $\Omega$ ...
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Understanding the Degrees of freedom of a Ballbot

A Ball Balancing Robot is dynamically stable robot capable of omnidirectional motion. It possesses non-holonomic properties and is a special case of underactuated system, classified as a Shape-...
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Holographic Degrees of Freedom

What does it mean when one says "holographic degrees of freedom" in dS space? As Susskind does in his recent papers, the latest here (page 18).
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Why is it that for electromagnetic waves, there are always two independent modes, or polarisations, per state? [duplicate]

Context I was looking for a good derivation of Planck's law. In [1], it states ``Finally, for electromagnetic waves, we are always allowed two independent modes, or polarisations, per state...'' ...
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How Many Degrees of Freedom of a Baseball Pitch?

My class asks why a major league pitch is so difficult to hit. A ball is pitched with adjustable velocity and trajectory, the latter dictated partly by spin (or on rare occasions, lack of spin). ...
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Pendulum constrained by a spring and generalized forces [closed]

I've been going through some problem sets used in a classical mechanics course offered a few semesters ago as a way to prepare for when I have to take that course next semester and I've hit a snag ...
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Modes of vibration of triatomic molecules

$$\omega=0,\sqrt{\frac Km},\sqrt{\frac{K(2m+M)}{Mm}}$$ There are three modes here but actually triatomic linear molecule have 4 vibrational modes (e.g. CO2). So where does that remaining one mode? ...
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How to count degrees of freedom

I am able to visualize and see that $y=A \sin{x}$ has 1 degree of freedom, because $z=0$ and $y$ depends on $x$. However, its plot looks like a 2D plane, even though according to the DOF it is a 1D ...
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What are the degrees of freedom of a dumbbell?

Edit 1: May be I should modify my question after getting the answers. I see why $(X_c, Y_c, Z_c, \theta, \phi)$ are legitimate Dof's of the dumb-bell, I never had any problem with that. Please ...
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How do the degrees of freedom change

I came across the following problem in an old exam: How many degrees of freedom does a system of 4 mass points (A,B,C,D) have, if the distances AB, BC and CD are given? So my attempt was to say ...
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What does it mean for a degree of freedom to come to thermal equilibrium?

I'm learning about diffusion speeds of particles in aqueous solution and the fundamental concept is thermal energy. The notes I'm working from say that "every degree of freedom comes to thermal ...
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Degrees of Freedom contributing to dynamic?

I had a question regarding considering how many degrees of freedom (dof), contributing to dynamics, a $\rm CCl_4$ Molecule has. In General there are 5 Atoms in the Molecule, so the maximum would be 15,...
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Is any artificial degree of freedom caused by the electrical current concept?

The electrical current concept multiplies together charge distribution and charge velocity distribution. It thus transforms two degrees of freedom into one. Combining two degrees of freedom into one ...
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How can one modify the Nambu-Goto action to include the longitudinal degrees of motion?

The Nambu-Goto action is given by $$ S = -\frac{T_0}{c} \int_{-\infty}^{+\infty} d\tau \int_{0}^{\sigma} d\sigma \sqrt{ \Bigg(\frac{\partial X^\mu}{\partial \tau} \frac{\partial X_\mu}{\partial \...
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Is the state of a system represented by a point $\textbf{q}=(q_1,q_2,q_3...q_n)^T$ in configuration space?

I was reading the lecture notes titled: 'An introduction to Lagrangian and Hamiltonian mechanics'. In these notes, he writes at one place: We consider mechanical systems that are holonomic and ...
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Massive Spin-1 Lagrangian: Removal of Spin-0 degree of freedom

I am currently reading Schwartz on QFT and the Standard Model and arrived now at Chapter 8.2.2, where he derives a Lagrangian for a massive Spin-1 field. The final Lagrangian looks like this: $$ \...
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Why do we not consider rotation as a Degree of Freedom in Monoatomic Gases?

I completely understand that the average energy of each degree of freedom in a thermodynamic system is (1/2)kT and that we do not consider the spin about an axis of symmetry in a polyatomic molecule ...
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Independent coordinates of a rigid body

This is a quote from Classical mechanics by Goldstein: "To fix a point in a rigid body, it is not necessary to specify its distances to all other points in the body ; we need only state the ...
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Why are constant volume and constant pressure heat capacities basically the same for solids? Are degrees of freedom involved?

I knowv that $C_V=\frac{\frac{f}{2} Nk_B}{m}$ and $C_P=\frac{(\frac{f}{2} +1)Nk_B}{m}$. Since for solids their values are very close to each other, I would assume $\frac{f}{2} +1$ is very close to $\...
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What is the proof of law of equipartition of energy?

In thermodynamics, law of equipartition of energy states that if we have any gas sample then the total kinetic energy will be distributed among the different degrees of freedom of the gas sample. Each ...
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3 votes
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What is the proof of $C_{V} = \frac{fR}{2}$?

I came across this formula in thermodynamics. Please give me a rigorous proof to this formula. My teacher did not even give any proof neither do any of my books. The formula is : $C_{V}=\frac{fR}{2}$ ...
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Why massless particles have less number of possible polarisations than massive ones? [duplicate]

It is stated that according to quantum field theory the value $0$ for the projection of the spin of the photon would be impossible because the photon has null mass, thus photon has two polarizations ...
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Electromagnetic waves how many polarizations for numberwaves?

I'm reading about stationary waves in a cube with side of length $L$. The electric field is described from a vector $E$ where each component is of the type $sin(\frac{\pi}{L}n_{j}x_{j})$ and the ...
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Degrees of Freedom of water and $\rm CO_2$ at high temperatures

How do I calculate the degrees of freedom for $\rm CO_2$ and water at high temperatures? I'm confused because I know $\rm CO_2$ is linear while H2O is nonlinear, and am wondering how this would affect ...
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How many degrees of freedom would water have at $\rm 500K$?

At this temperature, and lower, the rotational degrees of freedom would already be in action, then at this higher temperature id think vibration degrees of freedom are no longer frozen out. So this ...
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