60
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − '''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]]
Replacing page with 'your face'
your face