科研之友
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摘要
An elementary introduction to the adiabatic invariants of the Kepler problem is proposed. Unlike the other didactical expositions already present in the literature, which are based on the Hamilton-Jacobi theory of mechanics, our derivation is suitable to be grasped even by first-year undergraduates. A central role in the present analysis is played by an elementary proof of the virial theorem for the Kepler problem which is based on the chain rule for derivatives. As a byproduct of our analysis, an interpretation of Keplerian orbit eccentricities in terms of the time average of the position vector direction is also provided.
- 出版日期2013-9
