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Energy and Force Stepping Integrators in Lagrangian Mechanics

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Figure 2.1: Kepler problem. Exact, piecewise constant and piecewise linear continuous approximate potential energies.
Figure 2.7: Trajectories of argon atoms for a time window of [99.95, 100] nsec. The dashed line hexagon represents the initial position of the atoms
Figure 2.6: Frozen argon cluster. Top left: Energy-stepping. Top-right: Velocity Verlet, Δ𝑡 1 = 56.98 fsec
Figure 2.8: Convergence analysis of the frozen argon cluster. Left: Convergence is observed in the 𝐻 1 -norm with estimated convergence rate of 𝑟 ≃ 1/2
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Derivation of the Hamilton principle for the discontinuous energy stepping Frozen argon cluster Finite-element models Continuous piecewise linear representation of the approximate potential 𝑉 ℎ Conservation of momentum maps Convergence analysis Finite-element model with contact: oblique impact of neo-Hookean cube Conservation properties Chain of elastic beads

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