The Hamilton equations are a formulation of the equations of motion in classical mechanics.
are the Hamilton equations for the curve
Such a solution is called a bicharacteristic, and is called a Hamiltonian function. Here we use classical notation; the ’s represent the location of the particles, the ’s represent the momenta of the particles.
The most common case is when is the cotangent bundle of a manifold equipped with the canonical symplectic form , where is the Poincaré -form (http://planetmath.org/Poincare1Form). (Note that other authors may have different sign convention.) Then Hamilton’s equations are the equations for the flow of the vector field . Given a system of coordinates on the manifold , they can be written as follows:
|Date of creation||2013-03-22 14:45:58|
|Last modified on||2013-03-22 14:45:58|
|Last modified by||CWoo (3771)|