Hamiltonian Systems Introduction - Why Study Them?

Explore the foundations of Hamiltonian systems in this introductory lecture from a course on Hamilton's Equations. Delve into the Hamiltonian formalism, one of the two major pillars of mechanics alongside the Lagrangian approach. Discover the advantages of the Hamiltonian perspective and learn how to derive Hamiltonian systems from Lagrangian systems using the Legendre transformation. Examine key concepts such as generalized momentum, the Hamiltonian function, and Hamilton's canonical equations. Understand why Hamiltonian systems cannot have attractors and gain insights into their unique properties. This comprehensive lecture sets the stage for further study of advanced dynamics, nonlinear systems, and their applications in physics and engineering.

Lagrangian and Hamiltonian formalism of mechanics compared.
Advantages of the Hamiltonian formalism.
Hamilton's equations from Lagrange's equations.
Generalized momentum.
Hamiltonian function definition.
Hamilton's canonical equations and advantages.
Hamilton's canonical equations do not permit attractors.