Here is a guest lecture I have done last March at Aalto University for the course “Stability of Structures”, which was lectured by my late friend and inspirational figure Dr. Djebar Baroudi.

https://www.dropbox.com/scl/fi/k1kra0ojyhjxe1dwvp1c2/Lagrangian-mechanics.pdf?rlkey=ea0wlboqe1llhiauca3xnrpxm&dl=0

Title: “Lagrangian and Hamiltonian mechanics: formal aspects and engineering applications”

TOPICS:

PART I: FORMALISM

1.From Newtonian to Lagrangian Mechanics

2.The Lagrangian function

3.Generalized Coordinates, Momenta, and Forces

4.Hamilton Principle and Lagrange Equations

5.Hamilton equations and cyclic coordinates

6.Symmetry and Conservation Laws

7.Constraints and Friction Forces

8.Calculus of Variations and Lagrange Multipliers

9.Canonical Transformations and Hamilton-Jacobi Equations

PART II: APPLICATIONS

1.Fluid Mechanics

2.Chaos and Non-Linear Dynamics, including Bifurcations

3.Buckling of compressed elastic structures (nonlinear instability)

4.Structural collapse simulations

5.Aeronautical Engineering

6.Constructing Quantum Mechanics

7.Quantum Field Theory and Particle Interactions

8.General Relativity and Einstein Equations

9.Cosmology and Dark Matter