Conventional models of high velocity impact dynamics rely on approximate solutions of the governing partial differential equations for an elastic-plastic continuum, developed using weighted residual, finite difference, or other techniques prevalent in the computational mechanics literature. Hamiltonian mechanics provides an alternative approach, one which makes no reference to any PDE description of the physical system. The derived Hamilton’s equations incorporate general contact-impact effects, apply to a wide class of material constitutive relations, and allow for the simulation of highly nonlinear three-dimensional impact problems.
Hamilton’s Equations for Impact Simulations With Perforation and Fragmentation
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Horban, B. A., and Fahrenthold, E. P. (November 22, 2004). "Hamilton’s Equations for Impact Simulations With Perforation and Fragmentation." ASME. J. Dyn. Sys., Meas., Control. December 2005; 127(4): 617–622. https://doi.org/10.1115/1.2098879
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