All Questions
Tagged with dof or degrees-of-freedom
473 questions
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Issue with gauge transformation in photon polarization derivation
I'm trying to convince myself about a derivation of the two polarizations of the photon, but I'm stuck in last step.
Here is what I have done so far. I'm using as primary reference a post asked here ...
- 151
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2
answers
42
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Conjecturing the homogeneous solution of a $2^{nd}$-order constant coefficients ODE - why conjecturing a $3$ D.O.F. solution in this course?
In this video (MIT $8.02$ course titled "Electricity and Magnetism", video number $208$, taught by Pr. Peter Dourmashkin) professor solves the undriven $RLC$ circuit ODE ($2^{nd}$-order ...
- 740
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1
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22
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Driven $RLC$ circuit why is the permanent signal sinusoidal and why two degrees of freedom (amplitude and phase)?
In a second-order ODE with constant coefficients, with a sinusoidal RHS term (such as the ODE of the driven $RLC$ circuit), how do we know:
that the particular solution (i.e. the permanent signal) is ...
- 740
2
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2
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49
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Radiative and Longitudinal degrees of freedom of EM field
I'm having some issues trying to understand some of the affirmations my professor made in the last class. After working on the Maxwell's equation of the non-static regime for a quite a while, we ...
- 151
1
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1
answer
33
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Degrees of freedom of carbon dioxide based on quadratic energy terms
We all learned that by theorem of equipartition of energy, the quadratic terms in position or velocity components contribute to the number of degrees of freedom. Therefore, for a diatomic molecule, ...
1
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1
answer
56
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How to determine the nr. of degrees of freedom (for a system), for calculating the Lagrangian?
I want to have an understanding as what constitutes a degree of freedom of a system that we consider. My understanding of it, I believe, is pretty naive. I associate it with how an object moves in ...
- 1,628
2
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42
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Degrees of freedom for a bosonic closed string
I'm a newbie in string theory and I'm trying to get some insights about Polyakov action for the bosonic closed string, although my question isn't uniquely related with string theory: it is about ...
1
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1
answer
92
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Vibrational degree of freedom for monoatomic gases
I read that, when the temperature of a gas becomes high enough, a third type of degree of freedom becomes accessible, viz. the vibrational degree of freedom.
Also (at high temperatures) there is a ...
1
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2
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53
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Degree of Freedom and Equations of Motion [duplicate]
I am a bit confused about the number of degrees of freedom of a simple pendulum. Is there
only angular displacement, or
angular displacement and angular velocity?
Also, I am a bit confused on the ...
- 56
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0
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41
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Holographic principle with infinitely many degrees of freedom?
The holographic principle entails a limit to the number of degrees of freedom or possible states in a system (which would be givem by its surface rather than its volume, thus they would be "...
- 2,878
1
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0
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60
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About Yo-yo motion and forces constraint
The purpose of the Euler-Lagrange equation, is supposed to enable us to describe a system with the fewest possible coordinates, using generalized coordinates instead of traditional ones.
However, in ...
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0
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33
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Cells in phase space in Maxwell-Boltzmann statistical analysis of thermodynamics
Can't the states overlap? For example, for one particle the value of spread of its $p_x$ is 1 unit from $p_x=0.5$ to $p_x=1.5$ whereas, for the other particle, is 1 unit from $p_x=1$ to $p_x=2$. Isn't ...
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3
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84
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Do we consider a spring to be a constraint in classical mechanics. If yes/no why so?
I was brushing up on my DOF concepts before moving on to Lagrangian mechanics. One of my professors told me that a spring is not considered a constraint but his explanation was not satisfactory in my ...
4
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3
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590
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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 ...
- 303
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1
answer
34
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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^{\...
- 273
2
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90
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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?...
- 41
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58
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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-$...
- 53
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19
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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
6
votes
1
answer
511
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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. ...
- 542
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1
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43
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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 ...
- 11
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66
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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 ...
- 990
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56
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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 ...
- 4,157
2
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4
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166
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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 ...
- 109
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2
answers
73
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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, ...
0
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0
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221
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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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2
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203
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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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1
answer
158
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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 ...
- 49.4k
2
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5
answers
180
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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 ...
- 205
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56
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Regarding Degrees of Freedom and dynamics of polyatomic molecules [closed]
Justify how a molecule with N atoms have $3N-5$ vibrational degrees of freedom(Linear) and $3N-6$ vibrational degrees of freedom (Non-linear). Will this be valid for large number of N?
Taking $H_2O$ ...
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3
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72
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Doubt regarding kinetic theory of gases
My school teacher had told me that one of the assumptions of Kinetic Theory of Gases was that the molecules of a given gas were all identical and to be considered as very small elastic spheres. ...
- 123
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1
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86
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Difference between Kopp-Neumann and Dulong-Petit law?
So this is basically a follow-up to this question: How many degrees of freedom does the water molecule have?
I've done some further research and found that the main difference between Dulong-Petit and ...
- 85
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5
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2k
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Why expansion of real gases lead to cooling?
Paul Hewitt writes in his book
Expansion of real gases lead to cooling as average translational kinetic energy per molecule decreases.
The reason given is:
During Expansion molecules collide with ...
- 1,395
3
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2
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228
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Why the massive spin-1 photon gets more degrees of freedom than massless case; while the massive spin-1/2 electron stays the same as massless case?
Spin 1 field without mass term like photon has 2 real degrees of freedom. The polarization with two states. I think I can denote it as quantum state $|s,s_z> = |1,1>$ and $|1,-1>$.
Spin 1 ...
- 149
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1
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120
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Fermionic and bosonic degrees of freedom of a vector superfield
I am currently studying supersymmetry with the SUSY primer of Stephen P. Martin (https://arxiv.org/abs/hep-ph/9709356) and there seem to be not equally many bosonic and fermionic degrees of freedom (...
- 11
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1
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157
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Why does a degree of freedom vanish from 3D to 2D in that tensor construction?
Let's assume an arbitrary tensor in 3D coordinates: $g_{ij} $ with $i, j$ in $[1,3]$.
It shall be arbitrary, meaning not symmetric.
It has 9 entries which equals 9 degrees of freedom (dof).
Now, I ...
- 93
3
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1
answer
774
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The equipartion theorem and degree of freedom in case of vibration
I have been taught in chemistry that,
the energy of a vibrational freedom is $RT$ (ie, twice that of rotational/translational)
The degree of freedom which I found in chemistry, for the vibrational ...
- 63
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2
answers
149
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How can an object have more than 3 degrees of freedom?
In 1 of my robotics classes our professor told us that something can have up to 6 degrees of freedom:translation in the x axis , translation in the y axis,translation in the z axis,rotation around the ...
- 289
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1
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149
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On counting the DOF of EM wave polarization
I've got a few questions:
In a direvation I've seen, it's 4->3->2: in Lorenz gauge, by solving d'Alembert equation we get $A^\mu=\mathcal{A}\varepsilon^\mu e^{i(kz-\omega t)}$, and $\varepsilon^...
- 13
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1
answer
191
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How many relativistically invariant degrees of freedom in $n$-particle scattering?
Suppose we have a scattering process with $n$ external legs with four-momenta $p_1, \cdots, p_n$. Naively there are $4n$ degrees of freedom, however most of these putative degrees of freedom are not ...
- 820
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68
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Spin 3/2 field in higher dimensions
The Lagrangian and equation of spin 3/2 field in a general dimension D is given on page 96 of Supergravity ( textbook by Freedman and Proeyen, 2012 ). The action is :
$$ S = - \int d^Dx \bar{\psi}_{\...
- 542
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58
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Counting States for $N$ SUSY in Wess and Bagger [closed]
In Wess and Bagger's book, we calculate how many states are there for massive cases under $N$ SUSY.
We couldn't follow the table on page 14. What is "Spin" here (absolute value?), and how ...
- 41
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326
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Degrees of freedom in the early universe with MSSM?
As nicely summarized on P4 in On effective degrees of freedom in the early universe here; at high temperatures where all the particles of the Standard Model are present, we have 28 bosonic and 90 ...
- 1,496
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2
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366
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How many dimensions are in the electromagnetic field?
This question asks how many dimensions there are in the electric field for the purposes of better understanding polarization. However, the other answers don't seem to fully address the question, and ...
1
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1
answer
103
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How should we imbed massive spin-3 in a Lorentz covariant tensor? (degree of freedom-wise)
I'm not asking for Weinberg's systematic approach. Rather, I'm more concerned with how to get the correct degrees of freedom(dof) slickly for the moment.
I believe it should be imbedded in the rank 3 ...
- 631
3
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0
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115
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How many degrees of freedom does a photon have in 2+1D?
Wigner's classification of particles implies that the internal degrees of freedom of a particle transform under unitary representations of the subgroup of the Lorentz group that leaves its momentum ...
- 820
2
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1
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143
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Frenkel or Tulczyjew-Dixon Condition and QED
What is the physical motivation behind imposing Frenkel's condition,
$$p_{\mu}S^{\mu\nu}=0$$
for an electron of momentum $p$ and spin given by some tensor $S^{\mu\nu}$?
In addition, a direct ...
- 4,157
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259
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How many independent degrees of freedom does the metric tensor have in vacuum (at every point)?
A field of metric tensors fully characterises the curvature of a vacuum space-time. (For example, the spacetime between some single point masses which are themself not part of the manifold)
The metric ...
- 61
2
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1
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189
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Is there a general argument for why non-dynamical degrees of freedom show up in the propagation of massless gauge bosons?
In both spin-1 and spin-2 gauge theories, the gauge bosons (e.g. the photon & gluon and the graviton respectively) have two physical degrees of freedom, which can be observed quantum mechanically ...
- 820
1
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1
answer
148
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Deriving the gauge group from the little group
Arguments from the "little group" are used to show that the internal degrees of freedom of a massive particle transform under $SO(3)$, while the internal degrees of freedom of massless ...
- 820
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2
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91
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How did the number of unknowns change in the Dirac equation?
So I haven't seen this argument addressed in any textbook which makes me doubt it's legitimacy. Here goes:
Since Newton's $F=ma$ is essentially a second-order differential equation. Any equation of ...
- 1,349