lecture10: extensions: several dependent variables

Topics covered

• Extension
• Definitions
• Functionals
• Extremals
• Applying Taylor's theorem
• Deriving the Euler-Lagrange eq.s
• Simple example
• Example: movement of a particle
• The Lagrangian
• Hamilton's principle
• Generalized coordinates
• Example: a simple pendulum
• Kepler's problem of planetary motion
• Hamilton's principle and EL eq.s
• Newton's laws
• Conservation laws
• Example: a simple pendulum %
• Example: a simple pendulum
• Brachystochrone in 3D
• Kepler's problem of planetary motion
• Equations of planetary motion %
• Solving the equations
• Interesting aside
• Solving the equations
• Possible trajectories %
• %
• Geodesic on sort of gravity well shape