Multisymplectic Variational Integrators for Fluid Models with Constraints

Demoures, François; Gay–Balmaz, François

doi:10.1007/978-3-030-80209-7_32

Cited by 4 publications

(1 citation statement)

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“…Such discretizations, the RATTLE algorithm [11] and its generalizations [12][13][14] chiefly among them, typically exhibit superior long-term integration properties compared with standard, nonsymplectic integration algorithms, and have found wide application in the numerical integration of mechanical and control systems [15][16][17]. This approach has also been extended to the case of classical field theories with constraints [18,19], or to systems with dissipation [20]. What all these methods have in common is that they seek to enforce the constraint equations directly, which requires specialpurpose integration algorithms.…”

Section: Related Workmentioning

confidence: 99%

Feedback Integrators for Mechanical Systems with Holonomic Constraints

Chang

Perlmutter²,

Vankerschaver³

2022

Sensors

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The feedback integrators method is improved, via the celebrated Dirac formula, to integrate the equations of motion for mechanical systems with holonomic constraints so as to produce numerical trajectories that remain in the constraint set and preserve the values of quantities, such as energy, that are theoretically known to be conserved. A feedback integrator is concretely implemented in conjunction with the first-order Euler scheme on the spherical pendulum system and its excellent performance is demonstrated in comparison with the RATTLE method, the Lie–Trotter splitting method, and the Strang splitting method.

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