Theoretical Kaleidoscope pp 1-10 | Cite as

# Classical Mechanics. Unexpected Questions

Chapter

## Keywords

Dark Matter Variational Principle Oscillator Potential Canonical Momentum Orbit Radius
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## References

- Unfortunately, the known proofs of this simple fact are rather tedious.Google Scholar
- In the presentation here, we follow the note by
*I. B. Khriplovich, A. I. Milstein*(1999).Google Scholar - One should be warned against a possible naïve (and erroneous!) presentation of the Gauss theorem in the form
*Φ*(*r*) =*−kμ*(*r*)*/r*, where*Φ*(*r*) is the gravitational potential, and*μ*(*r*) = 4*π*∫^{r}_{0}*dr*1*r*^{2}_{1}*ρ*(*r*1) is the total mass of the matter inside the sphere of radius*r*. Obviously, if*μ*(*r*) grows with radius faster than*r*, such potential would result in antigravity, i.e., in the gravitational repulsion, but not attraction.Google Scholar

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© Springer 2008