## Hamiltonian Vector Fields?

##### September 17, 2024

Untitled Document In physics the primary object that we are often want to understand is the Hamiltonian111or Lagrangian of a system, denoted by H. Let M be the phase space of our system and so H:M→ℝ:(q,p)↦H(q,p). H gives rise to dynamics through Hamilton’s Equations dqdt=∂H∂p,dpdt=−∂H∂p. (1) While these equations can be thought of as just a system of PDES to be attacked, it is useful to think of them geometrically. ...