hamilton_jacobi - HAMILTON-JACOBI THEORY G OAL Find a...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HAMILTON-JACOBI THEORY G OAL : Find a particular canonical transformation such that the “new” Hamiltonian is a function only of the “new” momenta. M ATHEMATICAL PRELIMINARIES A canonical transformation may be derived from a generating function . Arguments of a generating function mix “old” and “new” variables. e.g., old momenta, new displacements S(q*,p) Differentiation yields “old” displacements and “new” momenta. p* = – ¡ S/ ¡ q* q = – ¡ S/ ¡ p Mod. Sim. Dyn. Sys. Hamilton-Jacobi theory page 1 There are three other possible generating functions: S(p*,q) q* = ¡ S/ ¡ p* p = ¡ S/ ¡ q S(q*,q) p* = – ¡ S/ ¡ q* p = ¡ S/ ¡ q S(p*,p) q* = ¡ S/ ¡ p* q = – ¡ S/ ¡ p Mod. Sim. Dyn. Sys. Hamilton-Jacobi theory page 2 “O LD ” H AMILTONIAN H(q 1 , ..., q n , p 1 , ... , p n ) To find the required transformation to the “new” variables, use a generating function S(q 1 , ..., q n , p* 1 , ... , p* n ) from which p j = ¡ S/ ¡ q j “N EW ” H AMILTONIAN...
View Full Document

{[ snackBarMessage ]}

Page1 / 5

hamilton_jacobi - HAMILTON-JACOBI THEORY G OAL Find a...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online