Classical Mechanics. Unexpected Questions

Part of the Lecture Notes in Physics book series (LNP, volume 747)


Dark Matter Variational Principle Oscillator Potential Canonical Momentum Orbit Radius 
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  1. Unfortunately, the known proofs of this simple fact are rather tedious.Google Scholar
  2. In the presentation here, we follow the note by I. B. Khriplovich, A. I. Milstein (1999).Google Scholar
  3. 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) = 4πr 0 dr1 r2 1 ρ(r1) 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
  4. See: L. D. Landau and E. M. Lifshitz, Mechanics. §15 (in particular, Problem 3).Google Scholar

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