Mathematical Classical Mechanics
Hamiltonian and Lagrangian formalism on symplectic manifolds.
Mathematical Classical Mechanics. Hamiltonian and Lagrangian formalism on symplectic manifolds.
Foundations and canonical references
The standard treatments of mathematical classical mechanics approach the subject from complementary angles. Arnold, Mathematical Methods of Classical Mechanics (1989) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Abraham, Foundations of Mechanics (1978) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for mathematical classical mechanics include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1989Mathematical Methods of Classical Mechanicsarnold-1989
- textbook · primary · 1978Foundations of Mechanicsabraham-1978, marsden-1978
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