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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Why potential energy is not considered in the internal energy of diatomic molecules?
In thermodynamics, I am taught that there are 5 degrees of freedom in diatomic molecules since there are 3 for translational and 2 for rotational. I interpret degrees of freedom as "ways you can ...
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Number of independent reparametrization gauge invariances of the 'world $(n+1)$-manifold action' of $n$-dimensional objects
As a generalization of point particle dynamics, one can conceive of a theory of $n-$dimensional objects with 'world-manifold' action given by
$$ S[X] = -\frac{T}{2} \int d^{n+1}\sigma \sqrt{h} h^{\...
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Why does $\rm{H_2 O}$ have 12 degrees of freedom?
I know there will be 3 translational D.O.F. and 3 rotational D.O.F., and it can have 4 vibrational D.O.F. (one potential and one kinetic) for each O-H Bond. But from where does 2 more D.O.F. come from?...
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Counting of degrees of freedom in Higher Spin Theories in curved spacetime
In 4d Minkowski, a (bosonic) tensor field with spin $s\in\mathbb{N}_+$ are constrained by Poincaré symmetry, and the physical degrees of freedom can be counted by considering the little group: a spin-$...
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Precise Definition of Degrees of Freedom [duplicate]
I am taking Analytical Mechanics and while reading Goldstein's and LL something bothered me: can I say that a degree of freedom is an independent (generalized) coordinate?
What bothers me is that we ...
user400821
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Electromagnetism in 2+1 dimensions?
Consider the Lorentz group $SO(2,1)$ in 2+1 spacetime dimensions. It's little group for massless particles should be just "$SO(1)$", which is just a trivial group with an identity element. ...
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Symmetry eliminates degrees of freedom
Consider a system of $n$ particles, such as isolated atoms, molecules, nuclei, and the solar system, with $3n$ degrees of freedom; why does translational invariance eliminate three degrees of freedom ...
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Degree of freedom - Lorentz transfomation reduces it? [duplicate]
I am having a real difficult to counting degree of freedom. In fact, I notice that sometimes I am confused about what exactly we count as DoF, and what we do not count.
See, for example, the ...
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Counting degrees of freedom in theories with two-forms [duplicate]
I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
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Is Bohr's model one-dimensional?
Purdue university in its article on Bohr's Model explains:
At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular ...
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Equal average energies in translational and rotational degrees of freedom
In, An Introduction to Thermal Physics, Schroeder states
It’s not obvious why a rotational degree of freedom should have exactly the same
average energy as a translational degree of freedom. However, ...
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How many degrees of freedom does a diatomic and triatomic molecule have at high temperatures?
I understand that a diatomic molecule has 3 translational and 2 rotational degrees of freedom. But since there is only 1 vibrational mode associated with a diatomic molecule and 1 vibrational mode is ...
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Is the equation for degrees of freedom $f=3N-k$ valid for all cases?
Consider the example of a linear triatomic molecule. Now at low temperatures, where we can exclude vibration, quite clearly degrees of freedom, $f=5$, with 3 translational and 2 rotational degrees of ...
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How many independent equations do Maxwell's equations represent in arbitrary dimensions?
In an arbitrary number of spacetime dimensions $D$, Maxwell's equations are
\begin{align*}
\mathrm{d}F &= 0, \\
\mathrm{d}(\star F) &= -J.
\end{align*}
How many independent equations does this ...
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Degrees of freedom in a molecule of $N$ atoms
I am trying to understand why the number of degrees of freedom in a molecule, $3N$, is the same as the number of degrees of freedom of $N$ independent particles. Why do the molecular constraints like ...
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