This course teaches advanced theoretical and semi-analytical tools for analyzing dynamical systems, particularly mechanical systems. The learning outcomes include understanding variational principles of mechanics, such as the Principle of Least Action and Lagrange's equations, and applying techniques in the calculus of variations to derive Euler-Lagrange equations. The course covers topics like Hamiltonian systems, nonlinear dynamics, periodic orbits, chaos, stability, and energy surfaces. The intended audience is individuals with prior knowledge of Lagrangian systems seeking a deeper understanding of dynamics and mechanics. The teaching method involves lectures, examples, and interactive tools to explore concepts like canonical transformations and generating functions.
Principle of Least Action and Lagrange's Equations of Mechanics - Basics of Calculus of Variations
Overview
Syllabus
Canonical transformations come from generating functions via variational principles.
Principal of least action.
Initial approach to understanding how principle of least action leads to Newton's equations.
Euler-Lagrange equations: More general, calculus of variations approach to principle of critical action, leading to Euler-Lagrange equations (Lagrange's equations in mechanics context).
Euler-Lagrange equations, example uses.
Brachistochrone problem.
Cubic spline curves (data fitting).
Taught by
Ross Dynamics Lab
