Transcription of Basic Hamiltonian mechanics - CERN
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Basic Hamiltonian mechanics - CERN
Potential V, independent of velocity, the Lagrangian takes the specific form: OCR OutputIn the simplest, non-relativistic case where the forces can be derived from a scalar2 . OUTLINE OF LAGRANGIAN AND Hamiltonian FORMALISMis then a function of 2k dynamical (qkvqk>t)necessarily, the time variable. The "Lagrangian" or Lagrange function L of the form:"velocity" co-ordinates qk = dqk / dt and the independent variable t, which is often, but notfreedom is characterised by a set of generalised "position" co ordinates qk, generalisedIn the Lagrangian formulation the dynamical behaviour of a system with lc degrees ofmotion of single particles, taking no account of the forces due to space covered by Jackson [2] in Chapter 12.
where dG is a total differential. This follows from Hamilton’s variational principle Pk dQk ‘ H1(Qk1PkJ)df- Ep), dqk — H(qk,pk,t)dr | = dGi\[k (26) OCR Output canonical is (qk,pk) and (Qk,Pk ). The necessary and sufficient condition for a transformation to be The form of the equations is preserved in transforming between co—ordinate systems
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