Abstract
The Lagrangian and Hamiltonian formalisms are among the most powerful ways to analyze dynamic systems. In this chapter we will introduce Lagrange’s equations of motion and discuss the transition from Lagrange’s to Hamilton’s equations. We write down the Lagrangian and Hamiltonian for a charged particle in an electromagnetic field, and introduce the Poisson bracket.
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References
H. Goldstein, J. Safko, C. Poole, Classical Mechanics, 3rd edn. (Wiley, New York, 1998)
L.D. Landau, E.M. Lifshitz, Mechanics, vol. 1, Course of Theoretical Physics (Elsevier Butterworth-Heinemann, Burlington, 1976). (translated from Russian)
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Stupakov, G., Penn, G. (2018). The Basic Formulation of Mechanics: Lagrangian and Hamiltonian Equations of Motion. In: Classical Mechanics and Electromagnetism in Accelerator Physics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-90188-6_1
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DOI: https://doi.org/10.1007/978-3-319-90188-6_1
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-90188-6
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