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Mathematics of classical mechanics, including Hamiltonian mechanics, Lagrangian mechanics, applications of symplectic geometry to mechanics, deterministic chaos, resonance etc.

32 votes
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Stability of the Solar System

Due to chaotic behaviour of the Solar System, it is not possible to precisely predict the evolution of the Solar System over 5 Gyr and the question of its long-term stability can only be answered in a …
Zurab Silagadze's user avatar
2 votes
1 answer
519 views

Invariance of the Noether charge

The paper http://epubs.siam.org/doi/abs/10.1137/1023098 (Generalizations of Noether’s Theorem in Classical Mechanics, by Willy Sarlet and Frans Cantrijn) mentions "an interesting property of the Noeth …
Zurab Silagadze's user avatar
4 votes

Egg-ovoid rolling down an inclined plane

This paper https://jeb.biologists.org/content/221/19/jeb178988 contains an experimental investigation of egg rolling. Theoretically, it seems "the relationship of egg shape to egg movement (e.g. rolli …
Zurab Silagadze's user avatar
0 votes

Regarding understanding differential geometry

Maybe the following books will be helpful: The Geometry of Physics: An Introduction, by Theodore Frankel. Geometry, Topology and Physics, by Mikio Nakahara. For a quick introduction into the subject …
Zurab Silagadze's user avatar