Hamiltonian: Difference between revisions

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The '''Hamiltonian''' is given by  
The '''Hamiltonian''' <ref>[http://dx.doi.org/10.1098/rstl.1834.0017 William Rowan Hamilton "On a General Method in Dynamics; By Which the Study of the Motions of All Free Systems of Attracting or Repelling Points is Reduced to the Search and Differentiation of One Central Relation, or Characteristic Function", Philosophical Transactions of the Royal Society of London '''124''' pp. 247-308 (1834)]</ref><ref>[http://dx.doi.org/10.1098/rstl.1835.0009 William Rowan Hamilton "Second Essay on a General Method in Dynamics", Philosophical Transactions of the Royal Society of London '''125''' pp. 95-144 (1835)]</ref>  is given by  


:<math>H (q,p,t) = \dot{q_i}p_i -L(q,\dot{q},t)</math>
:<math>H (q,p,t) = \dot{q_i}p_i -L(q,\dot{q},t)</math>
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and
and
:<math>\dot{q_i} =  \frac{\partial H}{\partial p_i}</math>
:<math>\dot{q_i} =  \frac{\partial H}{\partial p_i}</math>
==References==
==References==
<references/>
;Related reading
*[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html  Herbert Goldstein,  Charles P. Poole, Jr. and  John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] Chapter 8: The Hamiltonian Equations of Motion.
[[category: classical mechanics]]
[[category: classical mechanics]]

Latest revision as of 15:11, 18 May 2011

The Hamiltonian [1][2] is given by

where are the generalised coordinates, are the canonical momentum, and L is the Lagrangian. Using the Hamiltonian function, the equations of motion can be expressed in the so-called canonical form:

and

References[edit]

Related reading