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.