- Possibility of rewriting the equations of the Newmark integration scheme as a kind of a Hamiltonian formulation.
- Liouville theorem
- Discrete symplecticity (cf Sanz-Serna 1992).
- Proof of the symplecticity with three different relationships on the matrix of transformation, which is not classical maybe interesting !
- Simpson’s quadrature for a discrete Lagrangian, to obtain a quadrature not at the order 1 of the discrete Lagrangian, but at higher order. With this, the discrete action takes into account the degree of freedom in the middle of a time step. Les intégrateurs symplectiques ne conservent pas l’énergie, mais gardent l’énergie bornée.
B. Valette - Les oscillations gravito-élastiques de la Terre : une invitation à l’étude d’une classe de problèmes spectraux