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.
418
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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 ...
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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 ...
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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 ...
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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 of a spherical pendulum attached to a particle on a table
I have a problem concerning a system of two particles, each with mass $m$ and connected by a light rope of length $l$. The first particle moves on a smooth horizontal table at angle $\psi$ from a ...
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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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Extra degrees of freedom in toy spontaneous symmetry breaking model?
Consider a Lagrangian with a real scalar field $\varphi$ and massless vector field $A_\mu$ with field strength $F_{\mu\nu}$,
$$\mathcal{L} = -\frac{1}{2}\left(\partial\varphi\right)^2 - \frac{1}{4}F_{\...
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What are the properties of metric tensor? [duplicate]
It's frequently said that graviton has spin-2, so its wave function should have $5$ independent components. The metric tensor has $n^2=16$ components, but it obeys the following property:
\begin{...
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Dynamics: why do physicists include derivatives like $\dot{\theta}$ in the state space for a system like a pendulum?
I come from statistics, so my experience with physics is spotty, especially on some simple stuff. I have been working on some applications related to control theory lately, and was looking at some ...
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How is the number of restrictions determined from the configuration of molecules? [duplicate]
I saw a reference say that a triatomic gas can have 6 or 7 degrees of freedom depending on the position of the particles because this affects the restriction. Given the formula
$$ f = 3N - m $$
Where ...
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Why don't we use the "degree of freedom" as a factor in the ideal gas equation?
For an adiabatic process, the ideal gas follows the equation
$$ PV^{\gamma}= constant$$
The equation above implies that the pressure of an ideal gas (under adiabatic process) depends on the "...
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Proca equation gauge conditions
In massive case without any gauge conditions proca equation can be written as
$\partial_\nu(\partial^\nu A^\mu- \partial^\mu A^\nu)+\left(\frac{mc}{\hbar}\right)^2 A^\mu=0$
Since $A_\mu$ is a $n$-...
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How to calculate degrees of freedom?
Background
I am trying to run optimizations on a multilink (car-) suspension. That is each link is defined by two points, one on the vehicles body, one on the wheel mount. There are 5 links in total, ...
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Number of Independent Components of Levi-Civita Christoffel Symbol
Can anybody explain why Levi-Civita Christoffel symbol in general $N$ dimensional space have $\frac{N^2(N+1)}{2}$ independent components?
I have read that in $N$-dimensional space, metric tensor has ...
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How to know if the vibration system requires one degree of freedom or two? and how to pick the right coordinate to describe the movement?
I want to know a trick that helps me understand oscillatory systems and how to pick the correct general coordinates that describe the movement, I tried everything but I still can't get the solution ...
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Is there a way to calculate the number of degrees of freedom of water?
Say we have liquid water. We are given specific heat of water $C=4.2kJ(kg*K)$, a number of molecules in a mol $N_A=6*10^{23}$. The atomic weight of water is $18g/mol$, and the Boltzmann's constant is $...
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Does the degree of freedom change with speed for massive particle?
There are 2 degrees of freedom for a photon. But how many are there for massive particles and will this change with speed?
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Independent variables in thermodynamics
When we are dealing with a gaseous thermodynamic system, in books it's written that state of the system can be described by only two independent variables from the three $(p,V,T ) $. But it's not ...
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How many DOF does this system have?
I saw the problem above and thought it would be fun to solve it using lagrangians. However, in order to do this, one has to know the DOF of the system. And this is where it gets confusing for me. ...
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State of the art on Modified gravity : going beyond the 2nd order differential equations, diffeomorphism invariance breaking, extra degrees of freedom
I am going to do a state of the art on Modified gravity models. I have found a talk that presents the problematic. In particular, it is said the following things :
Modifying General Relativity
How to ...
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What is the degrees of freedom (Lagrange equation) of two connected spool rolling down two inclines?
I'm quite confused as to how to use the Lagrange equation [second type] in a system which features a spool rolling down an incline. I think this particular example is quite representative of what is ...
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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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3
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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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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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