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.
492 questions
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Degrees–of–freedom counting and Goldstone structure for $SU(3)$ broken by a complex $3\oplus\bar{3}$ Higgs
I am studying the Higgs mechanism in a single $SU(3)$ gauge theory with 2 scalars being a complex fundamental $\phi \sim 3$ and its complex conjugate $\psi \sim \bar{3}$. I would like to understand in ...
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Nr. of constraints and entries when considering coordinate transformation of the metric in GR
For the metric $g_{\mu\nu}$, when considering coordinate transformations, one can write:
$$g_{\alpha'\beta'}=\frac{\partial x^\mu}{\partial x^{\alpha'}}\frac{\partial x^\nu}{\partial x^{\beta'}}g_{\mu\...
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Why do “points” in phase space correspond to possible physical states of a system, rather than “lines”?
Why aren't “lines” the physical states of system, instead of “points”? In a simple harmonic oscillator, the motion of particles changes back and forth between kinetic and potential energy, but it ...
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Necessity for a $3N$ dimensional coordinate space in classical mechanics
The image is from Goldstein, Poole and Safko's book on classical mechanics. I do understand that the subscript $i$ on grad means taking the partial derivatives only with respect to the components of ...
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Gauge Invariance and Degrees of Freedom [duplicate]
According to Wigner's classification, any massless particle (except for scalars) has 2 degrees of freedom i 4D. This reduction is usually understood in terms of gauge invariance. For instance, a ...
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Definition of degrees of freedom in mechanics [duplicate]
At least in the context of Classical Mechanics and with no constrains, I have seen two radical different definitions of degrees of freedom:
One where the number of degrees of freedom is equal to the ...
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Phase line and its configuration space
If I consider a system represented by a phase line or a one dimensional phase space, which is the configuration space? Is the dimension of the configuration space zero? Can I consider this phase line ...
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State postulate
I have read that the state postulate says the state of a simple, compressible system is determined by any two intensive independent variables. Do such systems need to consist of a single phase and a ...
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In a simple, single-phase, single-component, compressible system, are $(p,V)$ sufficient to give a complete description of the system state?
I know that the state postulate applied to a simple, compressible, single-phase, single-component system means that any two independent intensive variables are sufficient to determine the state of a ...
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How is there a triple line on $p$-$V$-$T$ diagram for water, rather than a triple point?
If we consider the Gibbs phase rule
$$DoF(\text{Degree of Freedom}) = C - P + 2$$
for the case of water at its triple point:
$$C = 1\\
P = 3$$
Therefore we are left with $0$ degrees of freedom. So I ...
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Geometrical argument used in the calculation of degrees of freedom of a rigid body
We read in H. Goldstein's "Classical Mechanics" (2nd edition, p. 135) that
To fix a point in the rigid body, it is not necessary to specify its distances to all other points in the body; we ...
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On gauge theories and redundant degrees of freedom
Given an action or Lagrangian with the additional information that it is a gauge system, how do we know this field has how many physical or redundant degrees of freedom? Is there any systematic method ...
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Relation between DoF and Particles in General and Non-Relativistic Theory
Consider a field theory of a complex-valued scalar field,
$$
\mathcal{L}=\partial_\mu\phi^*\partial^\mu\phi-m^2\phi^*\phi
.$$
The field will obey KG equation. For such complex field, it is claimed ...
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Modes of motion: translation, rotation and ______? [closed]
Could there exist, and would it be possible to formulate conservation and motion laws of some 3rd "fundamental" type of motion?
To be clear what I want this 3rd (or more) type to be like, I ...
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Degrees of freedom of a massive vector field
For a vector field $A^\mu$, when we introduce a mass term, gauge invariance breaks and this leads to the appearance of a longitudinal polarization state in addition to the two transverse ones. This ...
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