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| − | '''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.
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| − | ==Hamilton's Equations==
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| − | 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]]:
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| − | <math>
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| − | \frac{dp_i}{dt}=-\frac{\partial H}{\partial q_i}
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| − | </math>
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| − | <math>
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| − | \frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}
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| − | </math>
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| − | [[Category:Physics]]
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| − | [[Category:Mechanics]]
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