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Results tagged with hamiltonian-mechanics
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user 54440
10
votes
1
answer
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Lifting a Diffeomorphism to the Cotangent Bundle
Both Abraham-Marsden and Da Silva seem to imply that given a symplectomorphism $g:T^\ast X\to T^\ast X$ which preserves the tautological $1$-form $\alpha$, it must be that $g$ is fibre preserving.
I …
- 243
2
votes
1
answer
592
views
Computation with the Legendre Transform
Let $M$ be a manifold and fix a Lagrangian $L\in C^\infty(T M )$. Let $x_1,\dots x_n$ be local coordinates for $M$ and equip the tangent bundle and cotangent bundle with standard coordinates $(x_1,\do …
- 243