Physics 321
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Physics 321 Hour 20 Hamiltonians
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Physics 321. Hour 20 Hamiltonians. whereas For simple systems, H = T + U There are two first order equations of motion for each variable: The Lagrangian method gives one second order equation for each variable. The Hamiltonian. Take Therefore. The Hamiltonian - Origins. Let - PowerPoint PPT Presentation
Transcript of Physics 321
Physics 321
Hour 20Hamiltonians
The Hamiltonian• whereas • For simple systems, H = T + U• There are two first order equations of motion for
each variable:
• The Lagrangian method gives one second order equation for each variable.
The Hamiltonian - OriginsTake
Therefore
The Hamiltonian - Origins
Let
If has no explicit time dependence, then H is a conserved quantity.
The Hamiltonian - Notes• The Hamiltonian is a function of p and q. But p is
not ‘the momentum,’ it is the generalized momentum conjugate to q.
• The general expression is:
• That means you generally have to find the Lagrangian before you can find he Hamiltonian!
The Hamiltonian - Notes• The Hamiltonian is H=T+U unless• The Lagrangian has explicit time dependence• The transformation between the coordinates
and Cartesian coordinates have explicit time dependence
• But … you have to write the Hamiltonian in terms of the correct generalized momenta – so you usually still need the Lagrangian first!
Examplehamilton.nb
