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A lot of good physics students here! When I was a student of physics and math for physics, the math was solid but often the physics had to be just swallowed wh
by graycat 3y ago
A lot of good physics students here!
When I was a student of physics and math for physics,
the math was solid but often the physics had to be just swallowed whole. This thread has some explanations missing from the physics sources I had!
I'm busy with my startup, but I'd like to see how the physics of Lagrange, Hamilton, Schrödinger, etc., e.g., least action, quantum mechanics, really work and to compare them with Newton's calculus of variations (the shape of the wire that would let a bead slide down in least time), deterministic optimal control (e.g., the book by Athans and Falb), Kuhn-Tucker optimization conditions, Lagrangians in optimization, etc.
- Cleonis 3y agoI created demonstrations with interactive diagrams. http://cleonis.nl/physics/phys256/calculus_variations.php http://cleonis.nl/physics/phys256/calculus_variations.php The following case is used as motivation for developing Calculus of Variations: the shape of a soap film stretching between two coaxial rings. (The name of the solution is 'catenoid'; a surface of revolution.) Then the discussion moves to the Catenary problem: to calculate the shape of a hanging chain. The two problems have the same solution; the curve is the hyperbolic cosine. Demonstration of Hamilton's stationary action: http://cleonis.nl/physics/phys256/energy_position_equation.php http://cleonis.nl/physics/phys256/energy_position_equation.p... The diagrams have sliders. Moving the sliders sweeps out variation of a trial trajectory. The diagram shows how the kinetic energy and the potential energy respond to sweeping out variation.