Hamiltonian

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

${\dot {p_{i}}}=-{\frac {\partial H}{\partial q_{i}}}$

and

${\dot {q_{i}}}={\frac {\partial H}{\partial p_{i}}}$

References

Related reading

• Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002) Chapter 8: The Hamiltonian Equations of Motion.