HAMILTON'S METHOD

Hamilton’s Method is a very efficient way of deriving the governing equations of a dynamic system. In this method one can ignore all the forces and moments that do not perform work. therefore, all the reaction forces and moments are eliminated from the problem automatically. This is the main advantage of analytical mechanics (including methods such as Lagrange’s Method) over Newtonian Mechanics. notice that Hamilton’s formulation is another form of writing the equilibrium equations or a systematic way of writing equilibrium equations in order to eliminate reaction forces and moments. For more examples, please refer to Bauchau [1] and Meirovitch [2].

The general form of Hamilton’s formulation is

where KE is kinetic energy, PE is potential energy, δw_nc is the virtual work due to non-conservative forces and moments.