摘要
According to the discrete Hamilton–Pontryagin variational principle,we construct a class of variational integrators in the real vector spaces and extend to the Lie groups for the left-trivialized Lagrangian mechanical systems by employing the spectral-collocation method to discretize the corresponding Lagrangian and kinematic constraints.The constructed framework can be transformed easily to the well-known symplectic partitioned Runge–Kutta methods and the higher order symplectic partitioned Lie Group methods by choosing same interpolation nodes and quadrature points.Two numerical experiments about the orbit propagation of Kepler two-body system and the rigid-body flow propagation of a free rigid body are conducted,respectively.The simulating results reveal that the constructed update schemes can possess simultaneously the excellent exponent convergence rates of spectral methods and the attractive long-term structure-preserving properties of geometric numerical algorithms.
基金
This work was supported by the National Natural Science Foundation of China(Grants 11772049,and 12132002).
