Hamilton's Principle Applied To Deformable Bodies
Hamilton's principle is an important variational principle in elastodynamics. As opposed to a system composed of rigid bodies, deformable bodies have an infinite number of degrees of freedom and occupy continuous regions of space; consequently, the state of the system is described by using continuous functions of space and time. The extended Hamilton Principle for such bodies is given by
where T is the kinetic energy, U is the elastic energy, We is the work done by external loads on the body, and t1, t2 the initial and final times. If the system is conservative, the work done by external forces may be derived from a scalar potential V. In this case,
This is called Hamilton's principle and it is invariant under coordinate transformations.
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