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Hamiltonian Dynamics (view source)
Revision as of 23:22, November 18, 2008
, 23:22, November 18, 2008New page: '''Hamiltonian dynamics''' is a formulation of mechanics that can be a useful alternative to Newton's formulation. It is closely related to [[Lagrangian Dynamics|Lagra...
'''Hamiltonian dynamics''' is a formulation of [[mechanics]] that can be a useful alternative to [[Isaac Newton|Newton's]] formulation. It is closely related to [[Lagrangian Dynamics|Lagrangian dynamics]], and makes use of the [[Lagrangian]] and [[Hamiltonian]] functions. From a mathematical viewpoint, problems in dynamics can sometimes be simpler to solve when written in the Hamiltonian formulation. The formulation is also important because it allows deep connections between [[Classical mechanics|classical]] and [[Quantum mechanics|quantum]] mechanics to be made.
==Hamilton's Equations==
Hamilton's equations are a set of 2n first order differential equations, which relate the co-ordinates <math>q_i</math> and the [[Momentum|generalized momenta]]:
<math>
\frac{dp_i}{dt}=-\frac{\partial H}{\partial q_i}
</math>
<math>
\frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}
</math>
[[Category:Physics]]
[[Category:Mechanics]]
==Hamilton's Equations==
Hamilton's equations are a set of 2n first order differential equations, which relate the co-ordinates <math>q_i</math> and the [[Momentum|generalized momenta]]:
<math>
\frac{dp_i}{dt}=-\frac{\partial H}{\partial q_i}
</math>
<math>
\frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}
</math>
[[Category:Physics]]
[[Category:Mechanics]]