lecture06: autonomous problems: the brachystochrone
Topics covered
- Euler-Lagrange equation
- Autonomous case
- Example: Brachystochrone
- Example: Brachystochrone (ii)
- Example: Brachystochrone (iii)
- Example: Brachystochrone (iv)
- Example: Brachystochrone (v)
- Cycloids
%
- Choosing the solutions
- Example: Brachystochrone solution
- Cycloids
- Meaning of $H$
- Newton's aerodynamic problem
- Newton's aerodynamical problem
- Alternatives: cylinder
- Alternatives: cone
- Alternatives: sphere
- Alternatives: frustum of cone
- Alternatives: optimal
- Alternatives: Haack series
- Typical shapes
- Bullets