On the design of non-singular, energy-momentum consistent integrators for nonlinear dynamics using energy splitting and perturbation techniques

This work proposes a suite of numerical techniques to facilitate the design structure-preserving integrators for nonlinear dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt difference quotient formula in their algorithmic force definitions, which suffers from instability as denominator gets close zero. There is need develop without invoking formula. In this work, potential energy Hamiltonian system split into two parts, specially developed quadrature rules are applied separately them. resulting can be regarded classical ones perturbed with first- or second-order terms, guarantees dissipative nature residual. meantime, conservation invariants respected design. A complete analysis proposed given, representative examples provided demonstrate performance. They used either independently energy-decaying momentum-conserving problems an alternate option conserving integrator, such when detected.