Editing Hamiltonian
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
The '''Hamiltonian''' | The '''Hamiltonian''' 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> | ||
Line 11: | Line 11: | ||
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.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]] |