Hamiltonian - Revision history

Carl McBride: Changed references to Cite format

2011-05-18T14:11:13Z

Changed references to Cite format

← Older revision		Revision as of 16:11, 18 May 2011
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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>
	==~~Recommended reading~~==
			==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.		*[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.
	~~==References==~~
	#[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)]
	~~#[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)]~~
	[[category: classical mechanics]]		[[category: classical mechanics]]

Carl McBride: Added Recommended reading section.

2008-04-10T15:59:37Z

Added Recommended reading section.

← Older revision		Revision as of 17:59, 10 April 2008
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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>
			==Recommended 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.
	==References==		==References==
	#[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)]		#[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)]
	#[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)]		#[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)]
	[[category: classical mechanics]]		[[category: classical mechanics]]

Carl McBride: /* References */ Added a couple of references.

2008-04-10T15:50:49Z

References: Added a couple of references.

← Older revision		Revision as of 17:50, 10 April 2008
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	:<math>\dot{q_i} = \frac{\partial H}{\partial p_i}</math>		:<math>\dot{q_i} = \frac{\partial H}{\partial p_i}</math>
	==References==		==References==
			#[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)]
			#[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)]
	[[category: classical mechanics]]		[[category: classical mechanics]]

Carl McBride at 11:12, 3 August 2007

2007-08-03T11:12:54Z

← Older revision		Revision as of 13:12, 3 August 2007
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	where <math>q_i</math> are the generalised coordinates, <math>p_i</math> are the canonical momentum,		where <math>q_i</math> are the generalised coordinates, <math>p_i</math> are the canonical momentum,
	and ''L'' is the [[Lagrangian]].		and ''L'' is the [[Lagrangian]].
			Using the Hamiltonian function, the equations of motion can be expressed in the so-called
			canonical form:

			:<math>\dot{p_i} = - \frac{\partial H}{\partial q_i}</math>
			and
			:<math>\dot{q_i} = \frac{\partial H}{\partial p_i}</math>
			==References==
	[[category: classical mechanics]]		[[category: classical mechanics]]

Carl McBride: New page: The '''Hamiltonian''' is given by : $H (q,p,t) = \dot{q_i}p_i -L(q,\dot{q},t)$ where $q_i$ are the generalised coordinates, $p_i$ are the canonical mome...

2007-06-25T11:29:05Z

New page: The '''Hamiltonian''' is given by :<math>H (q,p,t) = \dot{q_i}p_i -L(q,\dot{q},t)</math> where <math>q_i</math> are the generalised coordinates, <math>p_i</math> are the canonical mome...

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