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.

Filter by
Sorted by
Tagged with
2 votes
1 answer
61 views

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_{\...
0 votes
1 answer
66 views

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{...
0 votes
2 answers
75 views

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 ...
  • 157
0 votes
0 answers
10 views

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 ...
2 votes
2 answers
75 views

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 "...
  • 7,272
0 votes
1 answer
51 views

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 $n$-...
1 vote
0 answers
38 views

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, ...
  • 111
2 votes
1 answer
225 views

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 ...
1 vote
1 answer
34 views

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 ...
  • 11
0 votes
1 answer
76 views

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 $...
0 votes
1 answer
46 views

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?
  • 29
0 votes
2 answers
65 views

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 ...
0 votes
0 answers
44 views

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. ...
  • 309
0 votes
1 answer
86 views

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 ...
  • 1
1 vote
1 answer
55 views

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 ...
2 votes
1 answer
93 views

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 ...
4 votes
1 answer
105 views

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_\...
  • 14.5k
0 votes
0 answers
54 views

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 ...
  • 193
2 votes
1 answer
79 views

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 ...
0 votes
1 answer
109 views

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 ...
0 votes
1 answer
148 views

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 ...
3 votes
2 answers
119 views

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 ...
2 votes
2 answers
112 views

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 ...
1 vote
1 answer
90 views

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 ...
  • 2,403
4 votes
1 answer
140 views

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 ...
  • 3,879
1 vote
3 answers
114 views

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 ...
0 votes
1 answer
25 views

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 ...
  • 7
1 vote
2 answers
245 views

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 ...
1 vote
1 answer
89 views

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 $\mathbf{3}$, ...
  • 907
3 votes
4 answers
313 views

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 ...
0 votes
1 answer
144 views

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 ...
1 vote
3 answers
103 views

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 ...
  • 457
2 votes
2 answers
161 views

"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-...
  • 215
1 vote
0 answers
76 views

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 ...
0 votes
0 answers
37 views

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 ...
  • 53
4 votes
1 answer
83 views

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 ...
  • 111
2 votes
0 answers
85 views

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 ...
  • 907
0 votes
1 answer
151 views

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)...
0 votes
0 answers
86 views

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)...
1 vote
0 answers
46 views

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 ...
3 votes
0 answers
126 views

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 $\Omega$ ...
  • 9,840
2 votes
0 answers
129 views

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-...
0 votes
0 answers
47 views

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).
0 votes
1 answer
60 views

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...'' ...
-1 votes
1 answer
72 views

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). ...
4 votes
0 answers
146 views

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 ...
0 votes
3 answers
1k views

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? ...
0 votes
2 answers
285 views

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 ...
1 vote
4 answers
407 views

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 ...
  • 162
0 votes
1 answer
56 views

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 ...
's user avatar

1
2 3 4 5
9