All Questions
5
questions
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40
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Is there a way to express the collisionless boltzmann equation in terms of positions, velocities, times, without the distribution function?
Suppose I have data that represents a field of positions and velocities. If the distribution function (DF) for the data is $f(x,v,t)$, I know that the DF must obey
$$\frac{\partial f}{\partial t} + \...
1
vote
2
answers
158
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Why does the Lagrangian not show particle-interaction? Why are normal/tension forces not considered?
(1) For formulating a lagrangian for a system of particles compared to one free particle, we start with the kinetic energy and formulate a potential energy term that is in terms of each of the radius ...
- 17
3
votes
2
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897
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What is the "associated scalar equation" of equations of motion?
In an essay I am reading on celestial mechanics the equations of motion for a 2 body problem is given as:
$$\mathbf{r}''=\nabla(\frac{\mu}{r})=-\frac{\mu \mathbf{r}}{r^3}$$
Fine. Then it says the "...
- 1,517
3
votes
2
answers
855
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Bertrand's theorem
I found in Goldstein's Classical Mechanics that the condition for closed orbits is given by $\frac{d^2 V_{eff}}{dr^2}>0$.(bertrand's theorem). Can somebody explain to me, how this inequality is ...
- 1,880
0
votes
1
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191
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Non-relativistic Kepler orbits
Consider the Newtonian gravitational potential at a distance of Sun:
$$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$
I write the classical Lagrangian in spherical coordinates for a planet with mass $...
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