Calculus of variations: Euler–Lagrange equation and Hamiltonian formulation

Denny, Alessio Francis (A.A. 2021/2022) Calculus of variations: Euler–Lagrange equation and Hamiltonian formulation. Tesi di Laurea in Mathematics, Luiss Guido Carli, relatore Giovanni Alessandro Zanco, pp. 109. [Bachelor's Degree Thesis]

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Background theory of differential equations. Picard-Lindelöf general statement of the theorem. Intuition behind Cauchy sequences. Intuition behind Cauchy sequences of functions, pointwise convergence and uniform convergence. Complete proof of the Picard-Lindelöf theorem. Optimization intuition. First and second variation of a functional. The Euler-Lagrange equation derivation and intuition. Special cases of the Euler-Lagrange differential equation. The brachistochrone problem. The Hamiltonian. Integral, non-integral constraints and variable end-point problems.


Bibliografia: pp. 107-108.

Thesis Type: Bachelor's Degree Thesis
Institution: Luiss Guido Carli
Degree Program: Bachelor's Degree Programs > Bachelor's Degree Program in Management and Computer Science, English language (L-18)
Chair: Mathematics
Thesis Supervisor: Zanco, Giovanni Alessandro
Academic Year: 2021/2022
Session: Summer
Deposited by: Alessandro Perfetti
Date Deposited: 03 Nov 2022 15:34
Last Modified: 03 Nov 2022 15:34


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