Variational integrators for forced Lagrangian systems based on the local path fitting technique

•A new method is proposed to construct variational integrators for forced systems.•Variational integrators obtained by the new way inherit the benefit of existing ones.•The new approach significantly improves the precision of resulting integrators.•A detailed error estimation is attached to the construction of the integrator. Variational integrators are particularly suitable for simulation of mechanical systems, where features such as symplecticity and momentum preservation are essential. They also exhibit excellent long-time energy behavior even if external forcing is involved. Motivated by this fact, we present a new approach, that is based on the local path fitting technique, to construct variational integrators for forced mechanical systems. The core technology exploited is to fit the local trajectory as the Lagrange interpolation polynomial by requiring that the forced Euler–Lagrange equations hold at the internal interpolation nodes. This operation also yields the essential terms of the discrete forced Euler–Lagrange equations and consequently formulates the final integrator. This new approach not only avoids numerical quadrature involved in the classical construction, but also significantly improves the precision of the resulting integrator, as illustrated by the given examples.