Hamilton’s principle is a generalization of the principle of virtual displacements to dynamics. The dynamics version of the principle of virtual displacements, i.e. Hamilton’s principle, is based on...

Hamilton’s principle is a generalization of the principle of virtual displacements to dynamics. The dynamics version of the principle of virtual displacements, i.e. Hamilton’s principle, is based on the assumption that a dynamical system is characterized by two energy functions: a kinetic energy K and a potential energy W. Hamilton used the principle of D’Alembert, which asserts that any law of statics becomes transformed into a law of kinetics if the forces acting on the system are augmented by inertial forces, to extend the principle of virtual displacements to kinetics. Hamilton’s principle states that of all possible paths that a material particle could travel from its position at time t1 to its position at time t2, its actual path will be one for which the integral

where v is the velocity vector of a material particle in the body. Then, Hamilton’s principle can be expressed as

Use Hamilton’s principle to derive the equations of motion in Eq. (2.7.13) as the Euler– Lagrange equations. See Reddy [3, 13] for more details and examples of applications of Hamilton’s principle.