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Historical and Modern Perspectives on Hamilton-Jacobi Equations
Umeå University, Faculty of Science and Technology, Department of Physics.
2012 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

We present the Hamilton-Jacobi equation as originally derived by Hamilton in 1834 and 1835 and its modern interpretation as determining a canonical transformation. We show that the method of characteristics for partial differential equations, applied to the Hamilton-Jacobi equation, yields Hamilton's canonical equations and the action as the solution. Canonical perturbation theory is applied to the Sun-Earth-Jupiter system to calculate perturbations of the orbital elements. We also study tidal locking and find a damped harmonic oscillator equation for a moon that is almost locked. Finally, we present a modern (1980s), weaker notion of solutions to the Hamilton-Jacobi equation, viscosity solutions. We reproduce proofs that this concept is consistent with the classical concept and that visocsity solutions are unique, for locally Lipschitzian Hamiltonians.

Place, publisher, year, edition, pages
National Category
Physical Sciences
URN: urn:nbn:se:umu:diva-56269OAI: diva2:532943
Subject / course
Fysik C - Examensarbete
Educational program
Kandidatprogrammet i fysik och tillämpad matematik
Physics, Chemistry, Mathematics
Available from: 2012-06-14 Created: 2012-06-12 Last updated: 2012-06-14Bibliographically approved

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