Hamiltonian mechanics in 12 equivalent characterizations
What does Hamiltonian mechanics represent at the mathematical, geometrical and physical level? Here are 12 equivalent characterizations of Hamiltonian mechanics for one degree of freedom, that shows how the flow of states is the gradient of the Hamiltonian rotated 90 degrees, is incompressible, preserves area and, physically, it corresponds to deterministic and reversible evolution. #classicalmechanics #hamiltonian #symplecticgeometry #determinism
▶︎
The constitutive assumptions of Hamiltonian mechanics
▶︎
Geometric interpretation for all potentials (any dimensions!)
▶︎
FULLY REUSABLE Rocket Moves Closer to Launch! + Starship Flight 12 | This Week in Spaceflight
▶︎
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
▶︎
Local Dynamical Statistics of Entangled Quantum Systems
▶︎
Action principle: geometric and physical interpretation
▶︎
Lagrangian Mechanics: when theoretical physics got real
▶︎
The origin of Hamiltonian Mechanics
▶︎
No dissipative Lagrangians (or Hamiltonians)
▶︎
Newtonian/Lagrangian/Hamiltonian mechanics are not equivalent
▶︎
It's all about the entropy | #CORE1
▶︎
We can't prepare/measure infinity
▶︎
Lagrangian vs Hamiltonian Mechanics
▶︎
The equivalence between geometrical structures and entropy
▶︎
Trump Gets Booed and Falls Asleep at NBA Finals, Spreads Deranged CA Election Lies: A Closer Look
▶︎
Block on an Incline: Newtonian, Lagrangain and Hamiltonian Solutions
▶︎
The Tiny Donut That Proved We Still Don't Understand Magnetism
▶︎
Hamiltonian Physics Explained - Let's Learn Classical Physics - Goldstein Chapter 8
▶︎
But what is the Fourier Transform? A visual introduction.
▶︎