Lecture2

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PHY411 Lecture notes Part 2 Alice Quillen October 2, 2018 Contents 1 Canonical Transformations 2 1.1 Poisson Brackets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Canonical transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Canonical Transformations are ...

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...Phy lecture notes part alice quillen october contents canonical transformations poisson brackets are symplectic generating functions for example transformation action angle coordinates the harmonic oscillator some geometry tangent bundle dierential forms and wedge product form geometrically vectors generate flows trajectories hamiltonian ow two extended phase space ows preserve bracket on connection to lagrangian discretized systems integrators surfaces of section following a lie derivative examples orbits in plane galaxy or around massive body epicyclic motion jacobi integral shearing sheet symmetries conserved quantities that commute with noether s theorem integrability it is straightforward transfer coordinate using formulation as minimization can be done any system however hamil tonian only hamilton equations dened here those equivalently also search con served equivalent nice preserves consider function f q p t h where mo menta time dependence df fq fp dt we write this wecan short...

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Posted on: 28 Jan 2023 | 2 years ago
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